| Date | Speaker | Title & Abstract | Host |
| Aprl. 5 | Gabriel Stylianides (Oxford) |
Special Joint UCSD/MSED Colloquium Title: Supporting progressions in undergraduate students' justification schemes. Abstract: Students of all levels of education tend to have 'justification schemes' (Harel & Sowder, 1998) that are inconsistent with conventional validation methods. Yet, there is limited research knowledge about how mathematics instruction can support progressions in students' justification schemes so that they better approximate conventional validation methods. In this talk, I will draw on findings from a four-year design experiment in an undergraduate mathematics course to present and exemplify an instructional intervention that has been successful in supporting progressions in students' justification schemes. The notion of 'cognitive conflict' featured prominently in the theoretical framework that underpinned the design of the intervention. |
Jeff Rabin |
| Aprl. 12 | Sorin Popa (UCLA) |
Title:On the classification of II1 factors arising from free groups acting on spaces. Abstract:A famous problem of Murray and von Neumann (1943) asks whether the II1 factors L(Fn) associated with free groups with n generators, Fn, are non-isomorphic for distinct n's. While this problem is still open, its "group measure space" version, showing that the II1 factors L∞(X)⋊ Fn arising from free ergodic probability measure preserving actions Fn⤿ X are non-isomoprphic for n = 2, 3, ..., independently of the actions, has been recently settled by Stefaan Vaes and myself. I will comment on this, as well as on related results by Gaboriau, Ozawa, Ioana, Peterson. |
Adrian Ioana |
| Aprl. 19 | Peter Winkler (Dartmouth & MSRI) |
MSR Sponsored Colloquium Title: A Cop and Robber Solve the Kakeya Needle Problem. Abstract: We find optimal strategies for a pursuit and evasion game which, when pitted against each other, solve the problem of constructing a small area in the plane in which a unit-length line segment can be rotated. Joint work with Y. Babichenko, Y. Peres, R. Peretz and P. Sousi. |
Kristin Lauter & Microsoft Research |
| Aprl. 26 | Efim Zelmanov (UCSD) |
Title: Waring - type problems in Asymptotic Group Theory. Abstract: We will discuss the recent advances in the theory of profinite groups and their verbal subgroups. |
Math Dept. |
| May 17 | Ruth Williams (UCSD) |
Title: Resource Sharing in Stochastic Networks. Abstract: Stochastic networks are used as models for complex processing systems involving dynamic interactions subject to uncertainty. Applications arise in high-tech manufacturing, the service industry, telecommunications, computer systems and bioengineering. The control and analysis of such networks present challenging mathematical problems. In this talk, a concrete application will be used to illustrate a general approach to the study of stochastic processing networks based on deriving more tractable approximate models. Specifically, we will consider a model of Internet congestion control in which processing can involve the simultaneous use of several resources (or links), a phenomenon that is not well understood. Elegant fluid and diffusion approximations will be derived and used to study the performance of this model. A key insight from this analysis is a geometric representation of the consequences of using a "fair" policy for the sharing of resources. The talk will conclude with a summary of the current status and description of open problems associated with approximate models for general stochastic processing networks. |
Math Dept. |
| Date | Speaker | Title & Abstract | Host |
| Jan. 12 | Alan Reid (UT Austin) |
Title: Distinguishing Residually Finite Groups by Their Finite Quotients. Abstract: In broad terms this talk will discuss how much information about a f.g. residually finite group is carried by the collection of its finite quotients. For example a precise question in this direction (and which has been open for many years) is: Given a f.g. residually finite group G with the same collection of finite quotients as a free group of rank n, is G isomorphic to a free group of rank n? |
Alireza Salehi Golsefidy |
| Jan. 12 3 pm (please note special time) |
Brandon Rhoades (USC) |
Title: Cyclic sieving and cluster multicomplexes. Abstract: Let X be a finite set, C = ‹c› be a finite cyclic group acting on X, and X(q) ∈ N[q] be a polynomial with nonnegative integer coefficients. Following Reiner, Stanton, and White, we say that the triple (X, C, X(q)) exhibits the cyclic sieving phenomenon if for any integer d > 0, the number of fixed points of cd is equal to X(ζd), where ζ is a primitive |C|th root of unity. We explain how one can use representation theory to prove instances of the cyclic sieving phenomenon involving the action of tropical Coxeter elements on (complexes closely related to) cluster complexes. The representation theory involves cluster monomial bases of geometric realizations of finite type cluster algebras. |
Jeff Remmel |
| Tuesday Jan. 17 11:30p in 6402 (please note the special date and time) |
Jianfeng Lu (Courant) |
Title: Multiscale analysis of solid materials: From electronic structure
models to continuum theories. Abstract: Modern material sciences focus on studies on the microscopic scale. This calls for mathematical understanding of electronic structure and atomistic models, and also their connections to continuum theories. In this talk, we will discuss some recent works where we develop and generalize ideas and tools from mathematical analysis of continuum theories to these microscopic models. We will focus on macroscopic limit and microstructure pattern formation of electronic structure models. |
Bo Li |
| Jan. 19 | Ioan Bejenaru (Univ Chicago) |
Title: Equivariant Schroedinger Maps in 2D with large data. Abstract: I will introduce and motivate the Schroedinger Map problem. I will review the results obtain in the field. Then I will talk about the global regularity of equivariant maps in two dimensions with large data. |
Jacob Sterbenz |
| Friday Jan. 20 3p in 6402 (please note the special date and time) |
James McKernan (MIT) |
Title: Recent progress in the minimal model program. Abstract: Compact Riemann surfaces are naturally divided into three types; the Riemann sphere, elliptic curves and curves of higher genus. We will explain the conjectural analogue of this classification in higher dimensions, recent progress towards this classification and some open problems. |
Mark Gross |
| Friday Jan. 20 4p in 6402 (please note the special date and time) |
Elham Izadi (UGA) |
Title: Torelli problems. Abstract: Given a curve (Riemann surface), one can construct an abelian variety: its Jacobian. Abelian varieties are quotients of vector spaces by lattices. The classical Torelli theorem states that the Jacobian determines the curve. We discuss some generalizations of this and their history. |
Mark Gross |
| Monday Jan. 23 4p in 6402 (please note the special date and time) |
Zhiwei Yun (MIT) |
Title: Motives and the inverse Galois problem. Abstract: We will use geometric Langlands theory to solve two problems concerning number fields. One is Serre's question of whether there exist motives over Q with motivic Galois group of type E8 or G2; the other is the concrete question of whether there are Galois extensions of Q with Galois group E8(p) or G2(p) (the finite simple groups of Lie type), for sufficiently large primes p. The answer to both questions is "YES". |
Cristian Popescu |
| Feb. 2 | Frank Sottile (Texas A&M) |
MSR Sponsored Colloquium Title: Galois groups of Schubert problems. Abstract: Building on work of Jordan from 1870, in 1979 Harris showed that a geometric monodromy group associated to a problem in enumerative geometry is equal to the Galois group of an associated field extension. Vakil gave a geometric-combinatorial criterion that implies a Galois group contains the alternating group. These Galois groups are difficult to determine, yet they contain subtle geometric information. Exploiting Harris's equivalence, Leykin and I used numerical homotopy continuation to compute Galois groups of problems involving mostly divisor Schubert classes, finding all to be the full symmetric group. (This included one problem with 17589 solutions.) With Brooks and Martin del Campo, we used Vakil's criterion to show that all Schubert problems involving lines have at least alternating Galois group. My talk will describe this background and sketch a current project to systematically determine Galois groups of all Schubert problems of moderate size on all small classical flag manifolds, investigating at least several million problems. This will use supercomputers employing several overlapping methods, including combinatorial criteria, symbolic computation, and numerical homotopy continuation, and require the development of new algorithms and software. |
Kristin Lauter & Microsoft Research |
| Feb 16 | Sergey Kitaev (Univ Strathclyde) |
Title: Interval orders and related combinatorial objects. Abstract: A poset is called (2+2)-free if it does not contain an induced subposet that is isomorphic to the union of two disjoint 2-element chains. In 1970, Fishburn proved that (2+2)-free posets are in one-to-one correspondence with intensively studied interval orders. Recently, Bousquet-Melou et al. (M. Bousquet-Melou, A. Claesson, M. Dukes, and S. Kitaev, (2+2)-free posets, ascent sequences and pattern avoiding permutations, J. Combin. Theory Ser. A 117 (2010) 884-909.) invented so-called ascent sequences which not only allowed to enumerate (2+2)-free posets (and thus interval orders), but also to connect them to other combinatorial objects, namely to Stoimenow's diagrams (also called regular linearized chord diagrams which were used to study the space of Vassiliev's knot invariants), to certain upper triangular matrices, and to certain pattern avoiding permutations (a very popular area of research these days). Several other papers appeared following the influential work by Bousquet-Melou et al. Among other results, two conjectures, of Pudwell and Jovovic, were solved while dealing with (2+2)-free posets and ascent sequences. In my talk, I will overview relevant results and research directions. |
Jeff Remmel |
| Feb 23 | Fernando Rodriguez Villegas (UT Austin) |
Title: Combinatorics and Geometry Abstract: In this talk I will discuss a combinatorial calculation of the polynomial that counts the number of indecomposable representations of a certain quiver and dimension vector. I will start by introducing quivers, their representations and Kac's results and conjectures on such counting polynomials in general. The combinatorial calculation involves the reliability polynomial of alternating graphs. I will end with the main motivation for the calculation: its relation to the geometry of character varieties. |
Kiran Kedlaya |
| Mar. 1 | Cedric Villani (IHP) |
Special Joint Math-Physics Seminar Title: Landau Dampling Abstract: Landau damping is relaxation without dissipation. For more than a half century it has been considered as a key phenomenon in plasma physics, and studied both in physics and mathematics, however mainly at the linear level. In this lecture I explain about the physical and mathematical theory of Landau damping, and the recent progress by Mouhot and myself about Landau damping in the nonlinear, close-to-equilibrium regime. |
Peter Ebenfelt & Lei Ni & Tom O'Neil |
| Mar. 8 | Reserved | Reserved for Salah Baouendi's Memorial |
| Date | Speaker | Title & Abstract | Host |
| Oct. 13 | Pierre Colmez (Jussieu, visiting Berkeley) |
Title: Analytic continuation of L-functions. Abstract: I will explain how p-adic methods (the so-called p-adic local Langlands correspondence) can be used to prove the existence of an analytic continuation for complex L-functions. |
Kiran Kedlaya |
| Friday Nov. 4 (Please note special date) |
Ami Radunskaya (Pomona College) |
MSR Sponsored Colloquium Title: Random dynamical systems: is noisy growth better? Abstract: Many biological and physiological processes involve self-regulating mechanisms that prevent too much growth while ensuring against extinction: the rate of growth is somewhat random (``noisy"), but the distribution depends on the current state of the system. Cancer growth and neurological control mechanisms are just a few examples. In finance, as well, markets self-regulate since people want to "buy low" and "sell high". Some questions that we'd like to answer are: does the system have a well-defined average? In more technical terms, we want to know if the system is ergodic. How does this long-term average compare to the long-term behavior of the deterministic (not random) system? What can we say about the distribution of ``survival times", i.e. the distribution of times until the system reaches a particular value? In this talk we will look at (and listen to) a simple example of a noisy, discrete dynamical system with parametric noise and explore ways to answer these questions analytically. We prove ergodicity for a class of growth models, and show that the randomness is harmful to the population in the sense that the long-term average is decreased by the presence of noise. When systems obeying noisy growth laws are connected together as a coupled lattice, the long-term effects of the noise can have damaging effect on the organism as a whole, even though local interactions might favor growth in a particular area. We will present simulations that highlight the effect of both the noise and the local coupling on the survival of the organism. |
Kristin Lauter & Microsoft Research |
| Nov. 10 | Eric Friedlander (Northwestern & USC) |
Title: Lie algebras, subalgebras, and vector bundles (in characteristic p). Abstract: We discuss the challenge of understanding the WILD representation theory of Lie algebras over fields of positive characteristic. Even very explicit examples lead to difficult, if not impossible, problems. One can make some computations, but how does one give structure to these computations? Recent joint work with Julia Pevtsova introduces algebro-geometric invariants for such representations, an approach which leads to algebraic vector bundles on familiar (and not so familiar) algebraic varieties. |
Ruth Williams |
| Nov. 17 | Bob Pego (Carnegie Mellon) |
Title: Solitary waves and stability in fluids and particle lattices | Bo Li & Jacob Sterbenz |
| Dec. 1 11 am (please note the special time) |
Xinwen Zhu (Harvard) |
Title: Adelic uniformization of moduli of G-bundles Abstract: It is well-known from Weil that the isomorphism classes of rank n vector bundles on an algebraic curve can be written as the set of certain double cosets of GL(n,A), where A is the adeles of the curve. I will introduce such presentation in the realm of algebraic geometry and discuss two of its applications: the first is the Tamagawa number formula (proved by Gaitsgory-Lurie), and the second is the Verlinde formula in positive characteristic. |
Cristian D. Popescu |
| Dec. 1 3 pm (please note the special time) |
Herbert Heyer (Täubingen) |
Title: The embedding problem of probability theory revisited Abstract: One-parameter convolution semigroups of probability measures on Euclidean space are related to limits of partial products of infinitesimal triangular systems of measures, in the sense that such limits are embeddable into one-parameter convolution semigroups. It is a long-standing problem related to the central limit theorem that on an arbitrary locally compact group such a result cannot be tackled unless the infinitesimal system is commutative and additional conditions on the underlying group and/or the limiting measure are satisfied. We shall develop the main steps towards the solution of the problem of embeddable limits and connect the problem with the embedding of infinitely divisible probability measures on the group. The problem, in full generality, is still open. |
Patrick Fitzsimmons |
| Dec. 1 4 pm |
Sijue Wu (Univ of Michigan) |
Title: Wellposedness of the two and three dimensional full water wave problem. Abstract: We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time. |
Bo Li & Lei Ni |