Newsletter-2010




Newsletter of the Department of Mathematics
of The Ohio State University

Contents






Department Chair's message

Greetings to all colleagues, alumni, staff, students and general friends of the Department of Mathematics here at The Ohio State University: It is my great pleasure to be writing to you with news about our Department and University. There is, indeed, much exciting news to tell you.

Before discussing current news, however, let me salute the previous newsletters created by the Department. During the years 1984 to 1990, Professor Jim Leitzel edited and produced a newsletter that was a precursor to our current "Math Matrix". Moreover, in Spring 2006, the department also produced a newsletter/flier. Both of these may be found online (near the bottom) at http://www.math.ohio-state.edu/history

The past few years have seen immensely exciting change in the Department and at Ohio State. Indeed, it is a fabulous time to be both a Buckeye and a mathematician. Ohio State University is continuing to evolve into a superb educational institution; our students are becoming stronger every year (in terms of their scores on competitive exams like the ACT or SAT, etc.) and 2009 is no exception.

Our department has responded to these positive developments in many different ways as outlined in our "strategic plan" which was adopted two years ago. The strategic plan provides for specific changes during the years 2009-2013 involving, among other things:

  1. The creation of five new masters programs. These are: The Core Math Master (which begin in September, 2009), the Bio-Math Masters (which also began in September 2009), the Math Education Masters (to start in September of 2010), the Financial Math Masters (to start in September of 2011), and the Computational Math Masters (to start in September of 2012).
  2. Increased faculty contact with undergraduates.
  3. Designating some sections of certain classes as being only for math majors.
  4. Creating new math majors tracks in conjunction with the new masters programs. These are: The Core Math track, the Bio-Math track the Education track, the Financial Math track, the Applied Math track and the Applied Discrete Math track. These are in addition to our current actuarial program.
Certainly, the great efforts of the Department at teaching are having a very positive effect. Indeed, the numbers of our undergraduate majors have skyrocketed in the past few years from 323 in 2005 to over 600, currently, along with great growth in the numbers of our honors students. At the same time we have made impressive strides in the diversity of our students. Moreover, in the same time frame, our teacher training program has leapt from 320 students to 827 in 2008. And we fully expect these excellent trends to continue in the future.

All of this positive progress with our teaching mission could not, and would not, have happened without the great efforts of our staff, and vice-chairs supporting our programs. Indeed, this department is truly blessed by having devoted and gifted staff members at every level; from the MSLC (http://www.mslc.ohio-state.edu), to our Advising Office (http://www.math.ohio-state.edu/counseling). Similarly, our department has been wonderfully served by its vice-chairs: Dan Shapiro (vice-chair for instruction), Ulrich Gerlach (current vice-chair for undergraduate studies) as well as his predecessor Ron Solomon, Tom Kerler (vice chair for graduate studies) and Luis Casian (administrative vice chair).

Professor Casian, along with Jeff McNeal, who served as an associate dean for the past two years, also did a fantastic job with the budgets of the college and the department. We are very grateful to them for this impressive service.

The research mission of the Department of Mathematics has also improved greatly. There are also many indicators of this. First of all, the Department of Mathematics, together with our Mathematical Biosciences Institute (one of only 7 research institutes funded by the National Science Foundation; see http://mbi.osu.edu/) and the Department of Statistics, now ranks 4th nationwide in terms of overall National Science Foundation support for mathematical sciences. Considering the competition, this is no small accomplishment.

Secondly, our faculty have garnered many distinguished awards over the past few years. These are, in alphabetical order: Vitaly Bergelson (Distinguished Professor of Mathematical and Physical Sciences), Janet Best (2010 Sloan Fellowship), Herbert Clemens (2008 AMS Distinguished Service Award), Ovidiu Costin (Guggenheim Fellowship), Avner Friedman (University Distinguished Professor; SIAM fellow), Harvey Friedman (University Distinguished Lecture), Marty Golubitsky (SIAM fellow), Tadeusz Januszkiewicz (Banach Prize; Invited speaker for the 2010 International Congress of Mathematicians), Chiu-Yen Kao (Sloan Fellowship), Barbara Keyfitz (Saltzer Professorship), Jean-Francois Lafont (Sloan Fellowship), Jeff McNeal (elected Fellow of the AAAS), Stephen Milne (2007 Euler Medal), Henri Moscovici (Alice Louise Redenour Wood Chair), Neal Robertson (Fulkerson Award, 2009 and 2006), Akos Seress ( Australian Professorial Fellowship), Nimish Shah (Invited Speaker for the 2010 International Congress of Mathematicians) and Ron Solomon (Levi Conant Prize). Such great talent makes being chair a true pleasure.

Our department is also very fortunate to have a number of new regular faculty members recently join us. These are, again in alphabetical order: Nathan Broaddus, Ching-Shan Chou, Marty Golubitsky (who has succeeded Avner Friedman as the Director of the Mathematical Biosciences Institute), Ian Hamilton, Roman Holowinsky, Barbara Keyfitz, Nimish Shah, Joseph Tien and Hsian-Hua Tseng.

I would be remiss if I did not also tell those of you who have not been to campus recently about the changes occurring with the facilities here at OSU. Indeed, our facilities are improving right along with our students and our research. Here are some examples: In 2005, OSU opened the new recreations facility (the "RPAC"), which replaced the old Larkins Gym. The RPAC has four gyms, an aquatic center, and a great deal more. For those interested see http://www.recsports.osu.edu/facilities/recreation-physical-activity-cen... or go to Google Images and seach for "RPAC OSU photos".

Another remarkable building is the newly renovated main library, the William Oxley Thompson Library, which has just reopened this fall. The new Thompson Library is a beautiful, and highly functional, building that will be of great utility or our undergraduates, graduate students, and faculty. You can view the changes at http://libapp01.it.ohio-state.edu/about/locations/thompson-library/thomp...

Finally, our last example is the new Student Union now nearing completion, as of this writing, on the same site as the old union. This building also promises to be a great addition to the campus and is slated to open March 29, 2010; see http://ohiounion.osu.edu/new/

So there is much to be proud of here at the Mathematics Department and OSU! We will do our best to continue to keep you informed in future newsletters.

To the beginning


Departmental news



New faculty members


Nathan Broaddus

I received my Ph.D. from Columbia University in 2003.  I spent two years as a NSF Postdoc at Cornell University, followed by four years as an L.E. Dickson Instructor at the University of Chicago.  I joined the faculty of Ohio State University in the fall of 2009 as an assistant professor.

My work is in geometric topology, which includes geometric group theory and low-dimensional topology.  I am particularly interested in mapping class groups of surfaces and their relationship to automorphism groups of free groups and arithmetic groups.


Ching-Shan Chou I got my Ph.D. in the area of Applied Mathematics from Brown University. My thesis is about high order conservative schemes for hyperbolic conservation laws. I am currently working on computational and mathematical biology.

Martin Golubitsky

Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where he serves as Director of the Mathematical Biosciences Institute. He received his PhD in Mathematics from M.I.T. in 1970 and has been Professor of Mathematics at Arizona State University (1979-83) and Cullen Distinguished Professor of Mathematics at the University of Houston (1983-2008).

Dr. Golubitsky works in the fields of nonlinear dynamics and bifurcation theory studying the role of symmetry in the formation of patterns in physical systems and the role of network architecture in the dynamics of coupled systems. His recent research focuses on some mathematical aspects of biological applications: animal gaits, the visual cortex, the auditory system, and coupled systems. He has co-authored four graduate texts, one undergraduate text, and two nontechnical trade books, (Fearful Symmetry: Is God a Geometer with Ian Stewart and Symmetry in Chaos with Michael Field) and over 100 research papers.

Dr. Golubitsky is a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science (AAAS), and the Society for Industrial and Applied Mathematics (SIAM). He is also the 1997 recipient of the University of Houston Esther Farfel Award, the 2001 corecipient of the Ferran Sunyer i Balaguer Prize (for The Symmetry Perspective) and the recipient of the 2009 Moser Lecture Prize of the SIAM Dynamical Systems Activity Group. He has been elected to the Councils of the Society for Industrial and Applied Mathematics (SIAM), AAAS, and the American Mathematical Society. Dr. Golubitsky was the founding Editor-in-Chief of the SIAM Journal on Applied Dynamical Systems and has served as President of SIAM (2005-06).


Roman Holowinsky After four years of postdoctoral positions, split between the University of Toronto, the Fields Institute and the Institute for Advanced Study, I will be happily joining the Department of Mathematics at The Ohio State University in the Fall of 2010. My research is in analytic number theory with a current interest in developing analytic methods for automorphic forms on higher rank groups. My graduate work and thesis, Shifted Convolution Sums and Quantum Unique Ergodicity, was done under the direction of Henryk Iwaniec at Rutgers university.

Barbara Keyfitz
In January, 2009, I joined the Department of Mathematics at The Ohio State University, after 25 years at the University of Houston. From July 2004 until December 2008 I was Director of the Fields Institute for Research in Mathematical Sciences in Toronto, Canada. My research is in the field of nonlinear partial differential equations. I have studied systems of conservation laws which are nonstrictly hyperbolic or which change type from hyperbolic to elliptic in steady or unsteady flow. Systems with this behavior arise in models for multiphase flow in porous media, and in two-phase compressible and incompressible flow. With Suncica Canic and Eun Heui Kim, I began an analysis of self-similar solutions of systems of conservation laws in two space dimensions. Recently, I have been working with Katarina Jegdic and with Allen Tesdall on extensions of this multidimensional work.

Nimish Shah I joined the Department of Mathematics at the Ohio State University from September 2009 after 20 years at the Tata Institute of Fundamental Research in Mumbai, India. My main research interests are in the area of Lie groups and ergodic theory and their applications to number theory and geometry. More specifically we look for the role of symmetries and invariance groups in various number theoretic problems, and whenever possible reformulate such problems in terms of dynamical properties of subgroup actions on quotient spaces of Lie groups. In the course of my joint and independent works, we have successfully resolved several such problems, and in the process we have developed new general techniques to study the dynamical problems involving unipotent flows.

Joseph Tien I am broadly interested in mathematical biology.   My Ph.D. work at Cornell was in the area of dynamical systems, parameter estimation, and neuroscience.  I spent two years as a postdoc at McMaster University, where I studied mathematical epidemiology.   The current focus of my research is on waterborne diseases such as cholera.

Hsian-Hua Tseng Ph.D. University of California, Berkeley 2005, Dissertation: Quantum Riemann-Roch, Lefschetz and Serre Theorems for Orbifold Gromov-Witten Theory
My research interests fall into the general area of algebraic geometry and symplectic topology. I primarily study Gromov-Witten theory, especially for orbifold target spaces. On occasion I study questions related to birational geometry, especially on the existance of rational curves on singular varieties.

To the beginning


Some recent awards



Tadeusz Januszkiewicz awarded the 2008 Banach Prize

Polish Mathematical Society awarded its main 2008 Stefan Banach Prize for excellence in research to Tadeusz Januszkiewicz for his contribution to Geometric Group Theory ( http://www.ptm.org.pl/konkursy/banach/laureaci/). At the same time The International Stefan Banach Prize for a Doctoral Dissertation in the Mathematical Sciences (see http://www.banachprize.org/)  went to Tomasz Elsner. Tadeusz was also invited to speak at the ICM 2010 about the work he and his collaborators have done on simplicial nonpositive curvature. Tadeusz is leaving OSU and will work at the Mathematical Institute of Polish Academy of Sciences.



Ovidiu Costin awarded the 2008 Guggenheim Fellowship

Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts". Typically two or three fellowships are awarded each year to mathematicians in the US and Canada. Ovidiu Costin received a Guggenheim Fellowship in 2008. Five mathematics professors currently at Ohio State have received this award over the years: Ovidiu Costin, A. Friedman, H. Friedman, H. Moscovici and F. Tian.

Ovidiu Costin and his collaborators introduced new methods for studying general partial differential equations, the behavior of solutions of nonlinear differential equations in the complex domain and dynamical systems. Applied to the quantum theory of matter interacting with light, the methods provide formulas in cases where there are no reliable approximate methods or accurate numerical algorithms. The mathematical results explain a number of surprising effects observed experimentally. Recently, Ovidiu Costin together with his OSU PhD student M. Huang, obtained formulas describing the intricate shape of fractal sets.



Akos Seress awarded an Australian Professorial Fellowship

The Australian Research Council has awarded an Australian Professorial Fellowship to Akos Seress. His grant is one of the only two such fellowships with no teaching duties that were awarded this year in all disciplines. The title of the proposal was "Efficient computation in finite groups with applications in algebra and graph theory".

Professor Seress's major research area is computational group theory, in particular the design, analysis, and implementation of algorithms dealing with concrete representations of finite groups as permutation groups or matrix groups. He wrote a monograph on permutation group algorithms (Cambridge University Press, 2003) and recently with Babai and Beals proved a breakthrough result on the complexity of matrix group computations. He is a co-author of the computational algebra system GAP and wrote a significant portion of the permutation group algorithm part of the GAP library. He is also co-author of two GAP packages for matrix group computations.



Yuval Flicker has been selected as a recipient of a Senior Fulbright fellowship to present a series of lectures at the University of Buenos Aires

http://oia.osu.edu/global-perspectives/1576-global-perspectives-winter-2010-newsletter-.html

In June 2010 Yuval Flicker will travel to Buenos Aires, Argentina for three months to present a series of lectures to graduate students and faculty, and run a research seminar on current topics in arithmetic geometry at the University of Buenos Aires. His lectures will be based on his current research work with Pierre Deligne of the Institute for Advanced Study at Princeton. He will be describing arithmetic-geometric objects using analytic tools. His work revitalizes a work of Vladimir Drinfeld of Chicago, which has stayed dormant since 1981. "The work we are doing is revolutionary and opens a new area of research at the crossroads of algebraic geometry, arithmetic and representation theory – of very current interest. It was thought before that the technical difficulties were insurmountable, but we figured out how to open the door to advance the area, making it accessible to graduate students and other researchers. In retrospect, the initial observations were rather straight forward but were never realized," he said.

To the beginning


2010 International Congress of Mathematicians

The 2010 International Congress of Mathematicians will take place at Hyberabad, India. Nimish Shah and Tadeusz Januszkiewicz are invited to give talks at the Congress.



Nimish A. Shah: Equidistribution of translates of curves on homogeneous spaces and Dirichlet's approximation

Many problems in number theory involve more than one large groups of symmetries and invariance in a direct or an indirect manner. Understanding the dynamical interactions between these groups yield deeper insights into these problems. A new rapidly developing discipline of solving such number theoretic problems using ergodic properties flows on homogeneous spaces of Lie groups has taken shape during last 20 years.

I have been involved in this field since 1990 through my attempts to prove Raghunathan-Dani conjectures (1974) on algebraic rigidity of dynamics of unipotent flows in special cases, namely for Rank-1 Lie groups. During the special year (1991-92) at the MSRI (Berkeley) on Lie groups and ergodic theory, jointly with Eskin and Mozes we realized that a technique for counting lattice points on affine symmetric varieties as introduced by Duke, Rudnick and Sarnak (1991) can be combined with then new works of Margulis, Dani and Ratner about unipotent flows, and we could count lattice points on a large class of group varieties. The essential dynamical phenomenon involved in that work has turned out to be a very important concept in view of applications to other areas.

In my invited ICM 2010 talk, I plan to discuss my the recent results providing interesting and surprising observations on the above mentioned dynamical phenomenon which give new geometric results and resolve a conjecture due to Davenport and Schmidt (1969) about non-improvabiliy of Dirichlet's simultaneous approximation for related quantities.



Tadeusz Januszkiewicz: Simplicial nonpositive curvature

[Editorial comment: We hope we will be able to announce more details in the next issue of MATH MATRIX.]

To the beginning


The following graduate students received their PhD degree in 2008-2010


Ji Ye Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension (advisor - Saleh Tanveer) Lingfei Li Functoriality of harmonic foliations (advisor - Fangyang Zheng)
John McSweeney Time to coalescence for a class of nonuniform allocation processes (advisor - Boris Pittel) Ji-A Yeum Probability of soluability of random systems of 2-linear equations over GF(2) (advisor - Boris Pittel)
John Griesmer Ergodic averages, correlation sequences, and sumsets (advisor - Vitaly Bergelson) Sheng-Chi Liu Mass equidistribution of Hecke eigenforms on the Hilbert modular (advisor - Wenzhi Luo)
Rafal Pikula Enveloping semigroups of afine skew products and sturmian-like systems (advisor - Vitaly Bergelson) Peng Zhao Quantum variance of Maass-Hecke cusp forms (advisor - Wenzhi Luo)
Justin Young The twisted tensor L-function of GSp(4) (advisor - Stephen Rallis) Eric Swartz 2-arc transitive polygonal graphs of large girth and valency (advisor - Akos Seress)
Ronggang Shi Equidistribution of expanding measures with local maximal dimension and diophantine approximation (advisor - Manfred Einsiedler) Badal Joshi A doubly stochastic poisson process model for wake-sleep cycling (advisor - Janet Best)
Xueying Wang Mechanisms of simple perceptual decision making processes (advisor - David Terman) Kiam Heong Kwa Laser-driven charged particles as a dynamical system (advisor - Ulrich Gerlach)
Guo Luo Singularities in the complex spatial plane of a vortex sheet with blob regularization (advisor - Gregory Baker) Pasha Puliyambalathnaushad Lambda designs for lambda less than 60 (advisor - Akos Seress)
Zhi Qiu Study for the ionization of a quantum system with damped or undamped time periodic delta potentiall (advisor - Ovidiu Costin) Chao Xie Singularities in the uphysical complex plane for deep water waves (advisor - Gregory Baker)
Yang Yu A numerical approach for interfacial motion and its application to viscous effects in the Benjamin-Feir instability (advisor - Gregory Baker) Andriy Bezugly Reaction-diffusion-advection models for single and multiple species (advisor - Yuan Lou)
Kurt Oguz On the edge coloring of graphs (advisor - Neil Robertson) Christian Altomare Degree sequences, forcibly chordal graphs, and combinatorial proof sysems (advisor - Neil Robertson)
Niranjan Balachandran The 3-design problem (advisor - Neil Robertson) Suhkjin Hur The Kuratowski covering conjecture for graphs of order <9 (advisor - Henry Glover)
Martin Nikolov Construction of series of degenerate representations for GSp(2) and PGL(n) (advisor - Yuval Flicker) Christopher McClain Edge colorings of graphs and multigraphs (advisor - Neil Robertson)
Songyun Xu Degree 2 curves in the Dwork pencil (advisor - Herbert Clemens) Christian Schnell The boundary behavior of cohomology classes and singularities of normal functions (advisor - Herbert Clemens)
Wei Xiong Brownian Motion of a particle immersed in a viscous incompressible, Thermally Fluctuating Solvent (advisor - Peter March) Shaun Ault Symmetric homology is analog of cyclic homology in which cyclic (advisor - Zig Fiedorowicz)
Michael Khoury Multiplicity one results and explicit formulas for quasi-split p-adic unitary groups (advisor - James Cogdell) Scott Arms Minimal heights in number fields (advisor - Warren Sinnott)
Aditi Kar Discrete groups and CAT(o) asymptotic cones (advisor - Indira Chatterji) Keyan Yang On orbit equivalent permutation groups (advisor - Akos Seress)
Liang Niu The vertex primitive and vertex bi-primitive s-arc regular graphs (advisor - Akos Seress)

To the beginning


Undergraduate activities

Vitaly Bergelson

Undergraduates at Ohio State can get involved with mathematical ideas in a variety of ways, beyond our standard classes and honors classes. One excellent feature of our program is the Undergraduate Math Lounge, located in the basement of the math building. It provides a relaxed place for math majors to talk to one another, read math books, solve some interesting math problems, etc.

  • Our undergraduate math club Radical Pi, is organized by a group of math majors and meets several times per quarter. At each meeting, after some pizza and soft drinks, the presenter discusses some mathematical ideas, usually getting the audience members involved and talking. Several different sorts of people are asked to present some ideas, including faculty, postdocs, visitors, and students. Further information is posted on RadPI's web site: http://www.math.ohio-state.edu/undergraduate/radicalpi
  • In February every year we run Rasor-Bareis-Gordon Exam, a mathematics contest for OSU undergraduates. For more information (including the lists of winners, the problems which were offered in previous years etc) is provided at the RBG site: http://www.math.ohio-state.edu/undergraduate/RBG
  • Some of our best honors math students worked at Ohio State on summer research projects involving knot theory and combinatorics. This opportunity was made possible by the leadership of Sergei Chmutov, who ran the working group on Knots and Graphs. Here is a list of presentations by participants of the 2009 working group:
    • Robert Bradford:
      • The Young Mathematicians Conference (Columbus August 28-30, 2009).
      • The Shenandoah Undergraduate Mathematics and Statistics Conference (James Madison University, Harrisonburg, Virginia, October 3, 2009).
      • The 15th Annual Denman Undergraduate Research Forum, May 12, 2010.
    • Theodore Dokos:
      • The Shenandoah Undergraduate Mathematics and Statistics Conference (James Madison University, Harrisonburg, Virginia, October 3, 2009).
    • Jeffrey Lindquist:
      • The Young Mathematicians Conference (Columbus August 28-30, 2009).
    • Yishun Dong:
      • The Young Mathematicians Conference (Columbus August 28-30, 2009).
      • Scarlet and Great VIP Day (Columbus October 23, 2009).
    • Jack Cheng:
      • The 15th Annual Denman Undergraduate Research Forum, May 12, 2010.
  • The Reading Classics seminar was created by Warren Sinnott and myself, and has run every academic year since 2003. At this weekly seminar, students (both graduate and undergraduate) give presentations focusing on historical aspects of mathematics. Several students in this seminar have been actively engaged in translation projects.
  • The "What is?..." seminar was started last summer by Dan Shapiro and me, and we expect to continue it in future summers. The seminar met twice a week and attracted many graduate and undergraduate students who volunteered to present various topics not usually discussed in courses. Student papers from 2009 are posted at the seminar’s website: http://www.math.ohio-state.edu/whatis
  • RUMBA (Research for Undergraduates: adventures in Mathematical Biology and its Applications) is a recently established interdisciplinary activity, funded by the NSF. The program facilitates undergraduate research at the interface of mathematics and biology. More details appear at: http://rumba.biosci.ohio-state.edu/
  • Finally, let me mention two new honors courses that were developed recently and will be offered regularly to our honors students:
    • Rigorous probability, 531H
    • Honors combinatorics, (the pilot course under the number 594H will be taught by me in Fall 2010)
    More information on our many honors offerings is posted at: http://www.math.ohio-state.edu/counseling/HonorsProg.html

To the beginning


Events



Lecture series



Rado Lecture Series

Alain Connes of the Collège de France, Fields Medallist and winner of the 2000 Clay Research Award and the 2001 Crafoord Prize, presented the Rado Lecture series in the Ohio State Mathematics Department during the week of April 5-9, 2010. The 3-lecture series covered Connes' work on noncommutative geometry and its applications to theoretical physics and to number theory. The first lecture was a survey of the foundations of noncommutative geometry and index theory. The second lecture featured Connes' proposed unification of the standard model of particle physics with gravitation based on his spectral model of space-time. The third lecture dealt with his joint work with Katerina Consani on developing a framework for understanding mathematics in "characteristic one" using the theory of hyperrings and the applications of this method towards understanding the structure of the adèle class space of a global field.

  • Lecture 1: Noncommutative geometry and index theory
  • Lecture 2: The spectral model of space-time, gravity coupled with the standard model
  • Lecture 3: Primes and zeta, three variations on F1
The Rado Lectures were followed by a workshop during the week of April 11-16, covering these topics in greater depth for the benefit of graduate students and faculty. Talks in this workshop featured the following speakers from all over the world: A. Connes, H. Atsuoka, J. Borger, J. B. Bost, C. Chu, K. Consani, G. Cornelissen, M. Khalkhali, G. Landi, P. Lescot, J. Lopez Pena, O. Lorscheid, S. Mahanta, N. Minami, J. Morava, J. Plazas, N. Ramachandran, A. Salch, X. Tang, M. Vaqulé and Y. J. Yao.



Zassenhaus Lecture Series

Christopher Hacon of the University of Utah, co-winner of the American Mathematical Society's 2009 Cole Prize in Algebra, will present the Zassenhaus Lecture series in the Ohio State University Mathematics Department during the week of May 10-14, 2010. The 3-lecture series will begin with a presentation of the classical problem of finding a "canonical" projective representative for any given class of complex projective varieties that have the same field of rational functions and will culminate in a presentation of the recent solution of this problem obtained by Hacon and his collaborator (and Cole Prize co-recepient) James McKernan.

  • Lecture 1: Classification of complex algebraic varieties
  • Lecture 2: The minimal Model Program
  • Lecture 3: Boundedness of varieties of general type

To the beginning


Colloquia

In 2009-2010, our Colloquim speakers were:

  1. Robert Guralnick, University of Southern California
    research interests: algebra, particularly finite and algebraic groups and their linear and permutation representations. He applies group theory to study problems in arithmetic algebraic geometry, and Galois theory.
  2. Wilhelm Schlag, University of Chicago
    research interests: nonlinear partial differential equations. He studies hyperbolic equations arising in geometry and physics.
  3. Hillel Furstenberg, Hebrew University of Jerusalem.
    research interests: harmonic analysis, number theory, ergodic theory, topological dynamics. In the last decades he is was of the of the main forces in implementing the methods of ergodic theory in number theory and other areas of mathematics. He is a member of NAS, Israel academy of Sciences, and recent recipient of Wolf price.
  4. Eduardo Cattani, University of Massachusets at Amherst.
    research interests: algebraic geometry. His research was directed towards toric variety, Hodge theory and more recently on rational hypergeometric functions in several variables.
  5. Zhenghan Wang, Microsoft station Q at Santa Barbara, CA.
    research interests: topology and quantum computing. His research is directed on quantum topology, mathematical models of topological phases of matter, and their application to quantum computing.
  6. Gunther Uhlmann, University of Washington, Seattle (Walker family endowed professor).
    research interests: Partial differential equation, anlysis in general. His research targeted inverse problems, various aspects of microlocal analysis, scattering theory and applications.
  7. John Harer, Duke University.
    research interests: topology, computational topology, computational biology, algorithms. His resent research uses of geometric, combinatorial and computational techniques to study problems in shape recognition, image segmentation, biological networks and gene expression.
  8. Joel Smoller, University of Michigan (Lamberto Cesari Collegiate Professor).
    research interests: applied mathematics, differential equations, mathematical physics. His best known research is in shock-wave theory, Navier-Stokes equations, systems of reaction-diffusion equations; recently, has been concerned with problems involving gravity, as described by Einstein's Theory of General Relativity (GR).
  9. H. Blaine Lawson, SUNY at Stony Brook (Distinguished Professor).
    research interests: differential and algebraic geometry. He is best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles. Member of NAS and member of Brazilian Academy of Sciences.
  10. Constantin Teleman, University of California, Berkeley.
    research interests: Lie groups, algebraic geometry, quantum field theory.

To the beginning


The Young Mathematicians Conference 2009

[http://www.math.ohio-state.edu/conferences/ymc/]

Thomas Kerler

The sixth annual Young Mathematicians Conference (YMC) was held here in the Department during the weekend August 28-30, 2009. Seventy talented undergraduate students from all over the country participated, presenting a total of 43 talks and 16 posters on mathematical research projects in which they had been involved.

The selection process was more competitive than ever: A total of 160 students applied, but only 70 were selected for invitation and support, based on the review of their research abstracts by a panel of 20 mathematics professors. The majority of applications came from the already-selective Research Experiences for Undergraduates (REU) programs within the United States, of which there are only about 50. Topics of students' presentations included famous and subtle questions about L-functions in analytic number theory, isoperimetric inequalities in Riemannian geometry, categorical approaches to knot theory, problems about frame bundles in differential topology, and more topics in areas such as representation theory, class field theory, graph theory, and the theory of designs.

Among the presenters were OSU undergraduates Robert Bradford, Yishun Dong, and Jeffrey Lindquist, all of whom had participated in a summer workshop in knot theory organized by Professor Sergei Chmutov (OSU Mansfield) and held here in the Department.

A new event was introduced this year: the Outstanding Presentation Competition. First, second, and third prizes, as well as five honorable mentions were determined by both the ranking of the abstracts in the admission process as well as multiple visitations by senior participants during the conference itself. Certificates and small cash prizes were presented during the closing ceremony of the conference.

As in previous conferences, student participants were treated to three excellent plenary lectures by renowned mathematicians with distinguished research and expository credentials. Professor Peter Sarnak (Princeton and Institute for Advanced Studies) lectured on Diophantine analysis of apollonian packings, exploring the number theoretic mysteries of the integral curvatures occurring in circle packings in the plane. Professor Carolyn Gordon (Dartmouth) constructed, both mathematically and literally, drums which sounded alike but had different exotic shapes, concluding that You can't hear the shape of a drum. Professor Laura DeMarco (Illinois at Chicago) spoke on Finding stability in chaos, leading the audience through many real and mathematical examples of chaotic dynamical systems, and explaining how stability can manifest itself within these systems. The plenary lectures were received by students with enthusiasm and many questions. All three lectures were videotaped and are now available as video streams on the conference web site.

The Graduate School Orientation generated considerable interest among the visiting undergraduate students, most of whom are considering graduate work in mathematics. Representatives from PhD programs at several universities (including Ohio State) were on hand to discuss graduate study both in person and during an panel discussion on Sunday morning, addressing topics such as significance of scores, grades and letters in applications; how to choose graduate programs, topics, and advisors; and other support and career issues.

About a dozen REU mentors accompanied their invited students and actively participated in the program by chairing students' talks, evaluating talks for the Outstanding Presentation Competition, and joining the Sunday morning Mentor Breakfast, in which a variety of topics surrounding the organization and mentoring of undergraduate research were discussed.

The conference schedule provided plenty of opportunities for students to interact with each other and with plenary speakers, mentors, and graduate representatives. Frequent and lively conversations about topics both mathematical and otherwise arose during dinner banquets, poster sessions, and the numerous breaks between talks.

The conference received a great deal of local support. Eleven of our graduate students tirelessly helped with shuttle van driving, preparation of programs, participant lists, and other printed material, registration, technical assistance in presentation rooms, awards coordination, and numerous other miscellaneous errands. Our capable staff worked on the one hundred or so travel reimbursements, computer support, catering, and facility logistics. Department faculty also attended talks and social events and thus contributed to the life of the conference as well as the visibility of the Department within the undergraduate research community. Senior Associate Dean David Andereck and Chair David Goss gave the opening and closing addresses respectively.

The bulk of the financial support for the conference is provided by a three year grant from the National Science Foundation. Further funding was provided by our Mathematical Research Institute and generous donations from emeriti Frank Demana and Bert Waits.

The YMC has come a long way since its inception in 2003 under the Department's former VIGRE grant (another National Science Foundation program). Applicant numbers have quadrupled over the years. As reflected in mentor survey responses, YMC is now considered one of the premier undergraduate research conferences in the country along with events such as MathFest [http://www.maa.org/mathfest/] and Special Sessions for Research in Mathematics by Undergraduates at the annual Joint Mathematics Meetings.

Past plenary speakers include MacArthur and Sloan Fellows, Polya, Ostrowski, and Nevanlinna Prize winners, members of the National Academy of Science, and recipients of Haimo, Chauvenet, and Allendoerfer Awards.

Preparations for the seventh YMC (August 27-29, 2010) are in full swing. The plenary speakers will be Colin Adams (Williams), Bryna Kra (Northwestern), and Lauren Williams (Berkeley).

To the beginning


Conferences



Conference in Geometric Group Theory: "Davis 60", in honor of Mike Davis' 60 th birthday

The conference was held at the Mathematical Research and Conference Center in Bedlewo, Poland, June 14 – 20, 2009. The Conference Center is on a picturesque country estate outside of Poznan. Here is a link to the conference webpage, http://www.math.uni.wroc.pl/ggt/davis09 , where there are further links to pictures of the conference, and here is the link to the Bedlewo Conference Center, http://www.impan.pl/EN/Bedlewo/index.html . The two organizers from Columbus with Polish connections were Tadeusz Januszkiewicz and Swiatoslaw Gal.

There were 21 hour-long lectures on geometric group theory by Daniel Allcock, Uri Bader, Igor Belegradek, Mladen Bestvina, Noel Brady, Martin Bridson, Pierre-Emmanuel Caprace, Ruth Charney, Thomas Delzant, Alexander Dranishnikov, Cornelia Drutu, Tom Farrell, Mark Feighn, Frederic Haglund, Ursula Hamenstadt, Misha Kapovich, Guido Mislin, Thomas Schick, Karen Vogtmann, Kevin Wortman and Robert Young. During the afternoons there were many shorter talks. There were 118 registered participants.

Each night, except Thursday, the participants feasted at an outdoor barbecue with a large bonfire, a copious supply of beer, and mathematical expositions at a paper board in response to questions from graduate students and others. On Thursday the festivities included a banquet with a roast boar, a roast deer, a roast lamb, many speeches and a large amount of wine.






Noncommutative Geometric Methods in Global Analysis — conference in honor of Henri Moscovici ("Henrifest") at the Hausdorff Center for Mathematics

The conference description, from http://www.hausdorff-center.uni-bonn.de/event/2009/henrifest/ :

" Global analysis is a classical area of mathematics with a number of fundamental achievements to its credit. Noncommutative geometric methods, such as bivariant K-theory and cyclic cohomology, provided effective tools to analyze both classical and nonstandard spaces arising naturally in various parts of mathematics. In the earlier stages these methods found a number of important applications in global analysis, topology and representation theory. Very recent developments led to interactions with a number of other disciplines, including number theory and mathematical physics. Currently Noncommutative Geometry undergoes a period of vigorous growth and has been the breeding ground of interesting new ideas and developments.

The conference will honor Henri Moscovici on the occasion of his 65th anniversary, and in particular his fundamental contributions to the Noncommutative Geometry, Global Analysis and Representation Theory.

The conference will feature lectures by the leading experts in the area. There will be a special emphasis on the interactions between Global Analysis and Noncommutative Differential Geometry as well as connections with the other parts of mathematics, covering both the traditional directions and the newest trends in the subject. "






Ron Solomon honored at 2009 Skye Conference

The conference website: http://www.maths.abdn.ac.uk/skye2009/

A Conference on Algebraic Topology, Group Theory, and Representation Theory, funded by the Edinburgh Math Society, the L.M.S., and the N.S.F., was held on the Isle of Skye, Scotland, during the week of June 9 – 15, 2009. As a part of the conference, there was a banquet celebrating the 60th birthdays of Bob Oliver and Ron Solomon, whose research interests have unexpectedly converged on the study of fusion systems, a subject on the borderline between group theory and homotopy theory to which Bob has made major contributions recently. Ron discovered the only known examples of exotic simple fusion systems at the prime 2 while working on his dissertation. Our former colleagues, Radha Kessar (one of Ron's Ph.D. students) and her husband, Markus Linckelmann, both now at the University of Aberdeen, have investigated the connections between fusion systems and the modular representation theory of finite groups. Radha was one of the principal organizers of the Skye Conference, which brought together several more of Ron's former and current students – Andy Woldar, Inna Korchagina (also a conference organizer), and Justin Lynd. Also participating from O.S.U. were Mike Geline, Silvia Onofrei, and the entire Leary family. A conference highlight was the longest stretch of uninterrupted sunshine in recorded Scottish history.

Bob Griess, Dan Frohardt, George Glauberman, Michael Collins, Richard Lyons, Ron Solomon, Stephen D. Smith, Len Scott, Andy Woldar, Alex Turull Andy Woldar, Radha Kessar, Ron Solomon, Inna Korchagina, Justin Lynd Michael Aschbacher, Richard Lyons, Ron Solomon, Stephen D. Smith





A conference in honor of the 60th birthday of Harvey Friedman

was held at OSU on May 14-17, 2009; it was organized by Neil Tennant of the OSU Philosophy Department. Harvey Friedman is one of the world's leading researchers in the foundations of mathematics. The conference brought together a remarkable group of philosophers, logicians, mathematicians and computer scientists from across the country and Europe. For more information, see the conference web page http://people.cohums.ohio-state.edu/tennant9/friedman_conference.html, as well as the 2009-10 issue of Logos http://philosophy.osu.edu/news/logos/pdf/logos2009-10.pdf , the newsletter of the OSU Philosophy Department.

To the beginning


"O-minimal Structures and Real Analytic Geometry" program at Fields Institute

Prior to starting at OSU in Autumn 1997, faculty member Chris Miller spent January through June of 1997 at The Fields Institute as a funded postdoctoral researcher in a six-month program focussed on singularity theory and geometry. He was happy to return the favor by spending January through June of 2009 there as an organizer of such a program, "O-minimal Structures and Real Analytic Geometry". In brief, the focus was on the interaction of model theory (a branch of mathematical logic) and planar vector field theory. Over the last twenty-five years, the notion of o-minimal structure has become increasingly useful in the fields of real algebraic and real analytic geometry. First formulated by the model theorist L. van den Dries (Miller's Ph.D. advisor) in the early 1980s, this notion provides a unifying framework for what is sometimes loosely referred to as "tame" real geometry. Since then, the development of o-minimality has been strongly influenced by real analytic geometry. Conversely, model-theoretic methods available through the o-minimal point of view have led to new insights into real analytic geometry. For more detailed information, see the program's website.

To the beginning


Institute reports



Mathematics Research Institute

Jeff McNeal

The Mathematical Research Institute (MRI) has been a vital part of the research life in the Department of Mathematics since its founding in 1990. The purpose of the MRI is to enhance the ability of OSU faculty members and graduate students to interact with mathematicians from other leading universities. For almost 20 years, the MRI has fulfilled this purpose by funding the regular seminars run by the research faculty and by providing funds for many conferences and short-term visitors to the Department each year. These activities have led directly to numerous new collaborations between OSU and visiting mathematicians, as well as helping continue long-standing collaborative projects of the OSU faculty members.

In 2008 the MRI received an NSF grant and supplementary funds from OSU, which allowed it to add a series of "Special Year" programs to its list of sponsored activities. The Special Year programs are organized around two (or more) areas of mathematics where recently discovered interconnections have led to a surge of new results in these areas, and which connect with the research interests of some members of the OSU Mathematics faculty. The following programs have been run or are slated to run:

  • 2008-09: Analytic and Algebraic Geometry: the method of multiplier ideals. (Clemens, McNeal)
  • 2009-10: Noncommutative Geometry and Number theory: methods inspired by statistical mechanics. (Moscovici)
  • 2010-11: Geometric Group theory (Davis, LaFont)
It is hoped that other programs will be possible in the future.

The first Special Year program was a stimulating event. The participants viewed the workshops during this program as a truly productive exchange of ideas amongst mathematicians in Algebraic Geometry and Complex Analysis who only rarely travel in the same circles. A brief summary of the Special Year's activities is given below.

Special Year in Analytic and Algebraic Geometry, 2008–09

The 2008–2009 Special Year focused on the mathematical topics which formed the program for the Park City Mathematics Institute 2008, held in July 2008 and titled "Algebraic and Analytic Geometry: Common Problems – Different Methods". The goal of the Special Year was to develop the material from the advanced graduate courses of PCMI2008 in more detail than was possible during the PCMI program, thereby directly connecting participants to problems on the research frontier. Most of the participants in the 2008–2009 Special Year in our Department had also attended PCMI2008.

The centerpiece of the Special Year consisted of 5 week-long workshops for graduate students and young postdocs, conducted by experts from outside OSU in algebraic and analytic geometry. Workshops were held in October (Kollar), November (Berndtsson), January (Varolin), February (Lazarsfeld and Mustata), and May (Paun and Varolin), and were conducted by the mathematicians in parentheses. Over 75 graduate students and postdocs from outside OSU participated in these workshops, and about a dozen graduate students and faculty from OSU were active participants in all five workshops. Lecture notes, and lists of open and "warm-up" problems connected to the mathematics of each workshop, were distributed to all participants.

An additional activity of this Special Year consisted of a bi-weekly working seminar (totaling 4 hours per week) attended by the core OSU participants of the workshops mentioned above. This seminar ran from early September 2008 through May 2009. The foundation for the seminar was background material related to an upcoming workshop or extensions of material from a recently completed workshop. Finally, the Special Year 2008–2009 will conclude with the visit of Christopher Hacon in the spring of 2010, who will deliver the Zassenhaus Lectures in our Department under the title "Finite generation of the canonical ring".

To the beginning


The Mathematical Biosciences Institute

Marty Golubitsky

The missions of MBI are to provide a venue where mathematical scientists and biocientists can meet and work together and to expand the community of scholars in mathematical biology through education, training, and support of students and researchers. This mission is carried out primarily in two ways: through workshops and visitors and through the postdoctoral fellows program. In this report I will focus on workshops and visitors.

Workshops and Visitors

MBI has two types of workshops: emphasis year workshops (which take approximately three years to plan) and current topic workshops (which take about one year to plan). This year's emphasis year program is on Molecular interactions within the cell: Network, scale, and complexity. There will be six workshops related to this theme and four CTW: the dates, subjects, and anticipated speakers for these workshops can be found at: http://mbi.osu.edu/2009/scientific2009.html. Next year's theme will be on Evolution, synchronization, and environmental interactions: Insights from plants and insects. Preliminary details of the workshops associated with this program can be found at: http://mbi.osu.edu/2010/scientific2010.html.

Our planning of future MBI workshops is based on the fact that research at the interface between the mathematical and biological sciences flows in both directions. On the one hand, the mathematical sciences provide tools for the biological sciences that enable models to be both created and analyzed. This math → bio direction has been a staple of most MBI programs and it will continue to be a staple in the future. However, biology also offers the mathematical sciences new challenges and these challenges will surely lead to new mathematics and even to new fields in the mathematical sciences.

The two CTW in fall 2009 (Computational challenges in integrative biological modeling and Mathematical developments arising from biology) emphasized bio → math, the first on scientific computing issues and the second on the variety of mathematics areas that are impacted by the biosciences. MBI plans to emphasize more bio → math programs in the future and to do this MBI will increase the number of current topic workshops. So, the standard annual MBI portfolio will consist of six emphasis year workshops and six current topic workshops. CTW are flexible in style, format, and content.

MBI has both short and long-term visitors. The short-term visitors usually stay in Columbus for a few days to a week and are at MBI for one of the workshops. MBI has about 500 such visitors a year and these visitors can be found on the MBI website in the lists of participants of the various workshops. Long-term visitors are in Columbus for a period of at least one month and the current visitors are listed at http://mbi.osu.edu/visitors/current_visitors.html.

Ways to Interact with MBI

There are many ways in which math department faculty, post-docs, and students can interact with MBI. This year MBI is starting two new programs aimed in large measure at the local community including MBI visitors and postdoctoral fellows.

The first is the MBI Colloquium (most Monday's 2:30-3:30pm with tea afterwards). The Colloquium is interdisciplinary and aimed at the math, stat, bio, and biomedical communities in Columbus. Beginning this winter MBI will sponsor one course on a topic in mathematical biology each quarter. Marty Feinberg (Chem E, Math) will give the winter quarter course on Networks and Laura Kubatko (Statistics) and Dennis Pearl (Statistics) will jointly give the spring quarter course on Phylogenetics.

Here is a list of some of the many ways that math department researchers can interact with MBI.

  1. Register and participate in MBI workshops.
  2. Interact with MBUI short and long-term visitors.
  3. Attend individual talks (please consult the MBI Calendar and click on MBI Calendar at http://mbi.osu.edu/).
  4. View individual talks from your own computer (e-mail streaming@mbi.osu.edu to obtain the URL).
  5. Suggest speakers for the MBI Colloquium.
  6. Make suggestions for MBI workshops.
  7. Make suggestions for MBI long-term visitors (to be associated with emphasis year programs). Note that the 2011-12 emphasis year will be on Stochastics in biological systems and we are now beginning to plan long-term visitors.
  8. Apply for MBI course release (associated with emphasis year programs).

Ohio State is fortunate to have one of just seven NSF/DMS funded mathematical sciences institutes on its campus and MBI encourages local faculty to participate fully in its scientific programs.

To the beginning


Actuarial Science

Chunsheng Ban

Actuarial science is one of the two undergraduate major programs offered by the Department of Mathematics (the other major is, of course, mathematics). The goals of the curriculum in the Actuarial Science Program are twofold: (1) to supply a strong general background in mathematics, statistics, and relevant concepts from actuarial science and business, and (2) to prepare students to take some of the national actuarial examinations administered by the Society of Actuaries and the Casualty Actuarial Society.

In the last few years, we have seen a sharp increase in enrollment in actuarial science and a big improvement in the overall quality of our students. Currently, there are about 250 students in the actuarial program, and we have an increasingly higher percentage of students passing actuarial exams, getting OSU and outside scholarships, and getting internships and full-time employment offers. The high quality of our students has been recognized by the business; we have been receiving more and more positive feedbacks from employers which hire our students.

One important characteristic that distinguishes our program from many other institutions' is the close tie we establish with the industry. The collaboration takes many forms:

  • Practicum in Actuarial Science

    As an important part of a solid actuarial education, we have been offering a course in actuarial practicum. Actuaries from industry are invited to give lectures and conduct projects in their visits to the classes. In these projects, students work on problems in groups from different areas of actuarial practice to gain first-hand experience in an actuarial career. Visitors this spring included actuaries from Nationwide, STRS, Towers Perrin, Watson Wyatt, Mercer, Deloitt, and Aon.

  • Information Session

    Every year throughout the autumn quarter, we invite companies through the departmental Actuarial Club to come to the department to meet with students and conduct information sessions. Representatives from the actuarial industry give presentations to our students about actuarial careers in general and about their companies in particular. The information sessions are usually followed by on-campus interviews the next day by the visiting companies to recruit for their internship and full-time positions. Among the companies who visited us last autumn (2009) were Nationwide Financial, State Farm Insurance, Great American, Erie Insurance, Progressive Insurance, Mercer, Watson Wyatt, and Towers Perrin.

  • Fall Reception

    In order to create more opportunities for our students and in order to accommodate more companies and government agencies who want to meet our students, every autumn we hold a reception to bring students and representatives from business and government together. Through the reception, students learn directly from people working in the real world, and companies and government agencies become more familiar with our students and our program. Each year through this reception, the contact established between students and employers has led to many future offers of internships and full-time positions.

  • Financial Support

    We have been receiving financial support in different forms from business and non-profit agencies. The consulting firms Watson Wyatt and Towers Perrin (who have recently merged into the Towers Watson company) have been donating money for our program's operation and for scholarships. Great American, Angus Robinson, Jr. Foundation, and Griffith Foundation have also been offering scholarships to our students. For example, Great American has offered $6000 scholarship this year to our students and are coming in May to present the awards during our annual undergraduate recognition ceremony.

Facing the challenges of increasing enrollment and the need for curriculum for more advanced, better-prepared students, we are working hard to extend our industry connections, revise our existing courses, and develop new courses. Any help or suggestions from faculty, staff, and alumni would be much appreciated.

To the beginning


Alumni news



Radha Kessar awarded the 2009 Berwick Prize

Radha Kessar, an alumna of the Ross Summer Math Program and a 1995 Ohio State Ph.D., is the co-recipient with Joseph Chuang of the 2009 Berwick Prize of the London Mathematical Society. The Berwick Prize (formerly known as the Junior Berwick Prize) has been awarded by the L.M.S. in odd-numbered years since 1947 "in recognition of an outstanding piece of mathematical research published by the Society in the eight years before the year of the award." Previous recipients include Michael Atiyah, John Horton Conway, and George Lusztig. Radha and Joe share the award, presented on November 20th, for their joint paper, "Symmetric groups, wreath products, Morita equivalences, and Broue''s abelian defect group conjecture," Bull. London Math. Soc. 34 (2002), 174-184. The abelian defect group conjecture of Michel Broue' predicts a derived equivalence between the module category of a block B of a finite group algebra kG having an abelian defect group D and that of the Brauer correspondent block b of the normalizer kNG(D). The paper of Chuang and Kessar was a key ingredient in the proof of this conjecture for the family of all symmetric groups, a proof later completed by Chuang and Rouquier.

Radha first learned of Ohio State and Arnold Ross' Summer Math Program through Professor Ram Bambah, a family friend. After participating in the Ross Program, Radha returned to Ohio State as a graduate student in 1991, and became a Ph.D. student of Ron Solomon, completing a dissertation on source algebras of the spin covers of symmetric groups in 1995. After postdoctoral appointments at Yale, Minnesota, and Oxford, Radha and her husband, Markus Linckelmann, joined the Ohio State faculty in 2002, but were subsequently lured away in 2005 to help build a strong team of representation theorists at the University of Aberdeen.

To the beginning



We welcome news and information from and about Math Department alumni for inclusion in future issues of the Math Matrix; please mail us at mathmatrix@math.ohio-state.edu

To the beginning


Problem Corner


Another chance to try your problem solving skills! Send your solutions mathmatrix@math.ohio-state.edu. The best (or most interesting) solutions will be published in a future issue of Math Matrix. You are encouraged to submit problems for inclusion in this corner.



Problem 1.

Two people have 8 quarts of wine which is in an 8 quart jar. They also have an empty 5 quart jar and an empty 3 quart jar. How can they divide the wine equally?


Problem 2.

Find all prime numbers among 101, 10101, 1010101, 101010101, ... [from the 2009 Rasor-Bareis Examination]


Problem 3.

A plane has n seats. One of the passengers lost his boarding pass and doesn't know which seat is his; so, he is the first on board and seats himself into an arbitrary seat. Every other passenger sits at his assigned seat if it is unoccupied, and at a random empty seat otherwise. What is the probability that the last passenger will sit in his own seat, assuming that the plane is full? What is the probability that the kth to the last passenger will get his assigned seat? What are those probabilities if there are m passengers without a boarding pass?


To the beginning


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Last updated by leibman.1 on 08/18/10