Department of Mathematics,
University of California San Diego
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Algebra Seminar
Nolan Wallach
UCSD
$\bf{GK}$ Dimensions of $\bf{gK}$-modules
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AP&M 7218
AP&M 7218
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Department of Mathematics,
University of California San Diego
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Math 268 - Logic and Computation
Sam Buss
Toda's Theorem V
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AP&M 5402
AP&M 5402
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Department of Mathematics,
University of California San Diego
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Center for Computational Mathematics Seminar
Stefan Sauter
University of Zurich
Convergence Analysis for Finite Element Discretizations of Highly Indefinite Helmholtz Problems
Abstract:
\indent A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in $R^{d}, d=1,2,3,$ is presented.
General conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. As an application of the general theory, a full error analysis of the classical hp-version of the finite element method (hp-FEM) is presented where the dependence on the mesh width $h$, the approximation order $p$, and the wave number $k$ is given explicitly. In particular, it is shown that quasi-optimality is obtained under the conditions that $kh/p$ is sufficiently small and the polynomial degree $p$ is at least $O(log k)$. This result improves existing stability conditions substantially.
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AP&M 2402
AP&M 2402
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Department of Mathematics,
University of California San Diego
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Math 269 - Combinatorics
Mark Tiefenbruck
UCSD
Using an Extension of the Garsia-Milne Involution Principle to Find Bijections
Abstract:
\indent We will consider two recent open problems stating that
certain statistics on various sets of combinatorial objects are
equidistributed. The first, posed by Anders Claesson and Svante
Linusson, relates nestings in matchings of $2n$ points on a line to
occurrences of a certain pattern in permutations in $S_n$. The second, posed by Miles Jones and Jeffrey Remmel, relates occurrences of a large class of consecutive permutation patterns to occurrences of the same pattern in the cycles of permutations. We will prove an extension of the Garsia-Milne involution principle and use it to solve both problems.
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AP&M 7321
AP&M 7321
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Department of Mathematics,
University of California San Diego
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Math 268 - Logic and Computation
Sam Buss
Toda's Theorem VI
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AP&M 5402
AP&M 5402
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Department of Mathematics,
University of California San Diego
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Algebraic Geometry Seminar
Anton Geraschenko
When is a variety a quotient of a smooth variety by a finite group?
Abstract:
\indent If a variety $X$ is a quotient of a smooth variety by a finite group, it has quotient singularities---that is, it is \emph{locally} a quotient by a finite group. In this talk, we will see that the converse is true if $X$ is quasi-projective and is known to be a quotient by a torus. In particular, all quasi-projective simplicial toric varieties are global quotients by finite groups! Though the proof is stack-theoretic, the construction of a smooth variety $U$ and finite group $G$ so that $X=U/G$ can usually be made explicit purely scheme-theoretically.
\indent To illustrate the construction, I'll produce a smooth variety $U$ with an action of $G=\mathbb{Z}/2$ so that $U/G$ is the blow-up of $\mathbb{P}(1,1,2)$ at a smooth point. This example is interesting because even though $U/G$ is toric, $U$ cannot be taken to be toric. This is joint work with Matthew Satriano.
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AP&M 7218
AP&M 7218
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Department of Mathematics,
University of California San Diego
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Math 288 - Probability and Statistics Seminar
Tom Laetsch
UCSD
An $\bf{L^2}$ metric limit theorem for Wiener measure on manifolds with non-positive sectional curvature
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AP&M 6402
AP&M 6402
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Department of Mathematics,
University of California San Diego
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Mathematical and Numerical Relativity Seminar
Jim Isenberg
University of Oregon
Solutions of the Initial Value Constraint Equations of General Relativity
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AP&M 2402
AP&M 2402
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Department of Mathematics,
University of California San Diego
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Food For Thought Seminar
Alex Eustis
UCSD
Independence Number of Hypergraphs
Abstract:
\indent An $r$-graph is like a graph except that every edge contains $r$ vertices instead of two. We'll talk about how to find a large independent set in an $r$-graph, which means a set of vertices not containing any edge. Conversely, we'll also discuss how to generate a hypergraph where large independent sets do not exist. Some of research is joint with Jacques Verstraete.
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AP&M 7321
AP&M 7321
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Department of Mathematics,
University of California San Diego
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Informal Seminar on Mathematics and Biochemistry-Biophysics
Zhenli Xu
Department of Mathematics and Institute of Natural Sciences \newline Shanghai Jiaotong University, China \newline Department of Mathematics, UCSD
Image Effects in Colloidal Suspensions
Abstract:
\indent It is widely known the classical Poisson-Boltzmann theory fails to describe electrostatic interactions in the cases of multivalent counterions, highly charged surfaces, and low temperatures, as the theory ignores many-body ion-ion correlations. Surprising phenomena due to correlation effects include the charge inversion and the attraction between two likely charged colloids, both of which are recent focuses of theoretical and experimental study. In this talk, we will present some theoretical and simulation results on these problems by studying the role of image charges on spherical colloids, and discuss the method to include the correlation effects in the mean-field PB theory.
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AP&M 5829
AP&M 5829
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Department of Mathematics,
University of California San Diego
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Number Theory Seminar
Michael Skirvin
Northwestern University
Geometric Langlands and global Springer theory
Abstract:
\indent I will begin by giving a broad overview of the geometric Langlands progam, with emphasis on the local to global results of Beilinson, Drinfeld, Frenkel, and Gaitsgory. Their methods are particularly compelling because they do not have analogues in the original Langlands program. Using geometric Langlands as motivation, I will introduce the Hitchin fibration and describe recent results regarding the geometry of the global nilpotent cone (i.e., Hitchin fiber over zero). These results may be viewed in the
context of a global analogue of Springer theory, which suggests many future directions. If there is time, I will also explain relations to classical and higher rank Brill-Noether theory.
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AP&M 7321
AP&M 7321
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