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 Events
Kyle Hambrook
UBC
Mon 4 Mar 2013, 3:00pm
Harmonic Analysis Seminar
Math 126
The Sharpness of Mockenhaupt's Restriction Theorem
Math 126
Mon 4 Mar 2013, 3:00pm-4:00pm

Abstract

The Stein-Tomas restriction theorem says, essentially, that if \mu is the surface measure on the n-1-sphere in R^n (n \geq 2), then the Fourier transform is a bounded mapping from L^p(R^n) to L^2(\mu) for a certain range of exponents p. The range of exponents in the Stein-Tomas theorem is known to be sharp. Mockenhaupt's restriction theorem is a generalization of the Stein-Tomas theorem to more exotic measures on R^n. Izabella Laba and I have shown that the range of exponents in Mockenhaupt's theorem is sharp for the important case of Salem measures on R.

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Eldad Haber
Earth, Ocean and Atmospheric Sciences, and Mathematics, UBC
Tue 5 Mar 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Imaging of flow in porous media - from parameter estimation to prediction
ESB 4133
Tue 5 Mar 2013, 12:30pm-1:30pm

Abstract

Flow in porous media is difficult to model due to the non-linearity of the equations but more importantly, due to the lack of knowledge about earth parameters. In this talk we show how geophysical imaging can be used in order to compensate for the lack of information about the subsurface, and improve our ability to image and forecast subsurface flow.
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UBC
Wed 6 Mar 2013, 3:00pm
Topology and related seminars
ESB 4127
Relative twisting in Outer space
ESB 4127
Wed 6 Mar 2013, 3:00pm-4:00pm

Abstract

The notion of relative twisting of curves on a surface, the special case of subsurface projection to an annulus, is an important tool in the theory of mapping class groups. We develop an analogue for the outer automorphisms of a free group. This is joint work with Matt Clay.
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U. Kansas
Wed 6 Mar 2013, 3:00pm
Probability Seminar
ESB 2012
Malliavin calculus and convergence in density of some nonlinear Gaussian functionals
ESB 2012
Wed 6 Mar 2013, 3:00pm-4:00pm

Abstract

The classical central limit theorem is one of the most important theorem in probability theory.  The theorem states that if X_1, \cdots , X_n are independent identically distributed random variables and if F_n is the difference between the sample mean and the mean of the random variables properly normalized, then F_n converges to a normal distribution in distribution.  Recent results extend this results to other random variables for example given by Wiener chaos (multiple It\^o-Wiener integrals). In this talk, we shall obtain some conditions on F_n such that the distributions of the random variables F_n have densities f_n(x)  with respect to Lebesgue  measure and f_n(x) converges to the normal density \phi(x)=\frac{1}{\sqrt{2\pi}}e^{-|x|^2/2}.

The tool that we use is the Malliavin calculus and a brief introduction will also be given.

This is an ongoing joint work with Fei Lu and David Nualart.

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Institute for Advanced Study, Princeton
Thu 7 Mar 2013, 3:00pm
PIMS Seminars and PDF Colloquiums
ESB 2012
PIMS Public Lecture: Cryptography: Secrets and Lies, Knowledge and Trust
ESB 2012
Thu 7 Mar 2013, 3:00pm-4:00pm

Abstract

What protects your computer password when you log on, or your credit card number when you shop on-line, from hackers listening on the communication lines? Can two people who never met create a secret language in the presence of others, which no one but them can understand? Is it possible for a group of people to play a (card-less) game of Poker on the telephone, without anyone being able to cheat? Can you convince others that you can solve a tough math (or SudoKu) puzzle, without giving them the slightest hint of your solution? These questions (and their remarkable answers) are in the realm of modern cryptography. In this talk I plan to survey some of the mathematical and computational ideas, definitions and assumptions which underlie privacy and security of the Internet and electronic commerce. We shall see how these lead to solutions of the questions above and many others. I will also explain the fragility of the current foundations of modern cryptography, and the need for stronger ones. No special background will be assumed.

Bio:

DR. AVI WIGDERSON is a widely recognized authority in theoretical computer science. His main research area is computational complexity theory. This field studies the power and limits of efficient computation and is motivated by such fundamental scientific problems as: Does P=NP? Can every efficient process be efficiently reversed? Can randomness enhance efficient computation? Can quantum mechanics enhance efficient computation? He has received, among other awards, both the Nevanlinna Prize and the Gödel Prize.


Note for Attendees

A reception will be held in the PIMS Lounge, ESB 4133 at 2:30 p.m. Undergraduate and Graduate Students are welcome and invited to attend.
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Institute for Advanced Study, Princeton
Fri 8 Mar 2013, 3:00pm
Department Colloquium
MATX 1100 PIMS/UBC Distinguished Colloquium
The power and weakness of randomness (when you are short on time)
MATX 1100 PIMS/UBC Distinguished Colloquium
Fri 8 Mar 2013, 3:00pm-4:00pm

Abstract

Man has grappled with the meaning and utility of randomness for centuries. Research in the Theory of Computation in the last thirty years has enriched this study considerably. I'll describe two main aspects of this research on randomness, demonstrating respectively its power and weakness for making algorithms faster. I will also address the role of randomness in other computational settings, such as space bounded computation and probabilistic and zero-knowledge proofs.
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Sauder School of Business, UBC
Tue 12 Mar 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
A Fluid Model for an Overloaded Queuing System with Scoring-Based Priority Rules
ESB 4133
Tue 12 Mar 2013, 12:30pm-1:30pm

Abstract

We consider a queuing system with multi-type customers and servers. When a server is available, each customer is assigned a score which depends on the customer's waiting time, type, and the server's type. The service is then provided to the customer with the highest score. We develop a fluid limit process to approximate the behavior of such a system. Our model has two important features: (1) the service rate in the transient state coincides with the max-flow of a parameterized network; (2) the service rate at the steady state coincides with the the minimal-cost max-flow of a capacitated network. Thanks to these properties, we may solve the transient and stationary behavior of the fluid limit process efficiently by combinatorial methods, and predict the performance of the system when a scoring policy has been implemented. By properly defining the performance metrics, we may solve the scoring formula that leads to the optimal efficiency-fairness tradeoff. We illustrate the application of our fluid model in the context of kidney allocation policy design. In particular, the fluid model we developed can be used to predict the steady-state allocation outcome of the scoring policy proposed by the United Network of Organ Sharing (UNOS) in 2008.

 

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Remi Schweyer
Universite de Toulouse
Tue 12 Mar 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
Blow up dynamics for the 1-corotational energy critical harmonic heat flow
ESB 2012 (in the new PIMS building)
Tue 12 Mar 2013, 3:30pm-4:30pm

Abstract

After a short presentation of the equation of harmonic heat flow and corotational solutions, I am presenting a result of finite time blow-up dynamics. We will have to see how similar results for wave maps and Schrödinger map allow us to conjecture the instability of this regime in the general case. Finally, I will give a strategy of the proof.
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UBC
Wed 13 Mar 2013, 3:00pm
Topology and related seminars
ESB 4127
A topological approach to orderable groups
ESB 4127
Wed 13 Mar 2013, 3:00pm-4:00pm

Abstract

Algebra and topology are old friends. Many topological problems are solved by applying algebraic methods.  But sometimes the relationship can work the other way. My talk will discuss how the topological viewpoint can be used to establish the basic facts regarding orderability of groups.
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UBC
Wed 13 Mar 2013, 3:00pm
Probability Seminar
ESB 2012
Critical Quantum Random Graphs
ESB 2012
Wed 13 Mar 2013, 3:00pm-4:00pm

Abstract

We study the behavior of the so-called quantum random graphs inside the "scaling window". The quantum random graphs were first introduced by Ioffe and Levit 
in 2007 and they turn to be a certain generalization of the Erdős–Rényi random graphs. We show results for the quantum random graphs which are analogous 
to those of Aldous (1997), who proved that inside the "critical window", the rescaled sizes of components of the Erdős–Rényi graphs converge to lengths 
of excursions of a certain process related to Brownian motion.

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Brian Marcus
UBC
Thu 14 Mar 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Factor Graphs, Belief Propagation and Message Passing Algorithms
Math Annex 1102
Thu 14 Mar 2013, 2:30pm-4:00pm

Abstract

This is the first of two talks on the subject given in the title.

These talks are part of the informal learning seminar on Information, Physics and Computation, based on the book by Mezard and Montanari.
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Centre de Recherches Mathematiques
Thu 14 Mar 2013, 3:00pm
Number Theory Seminar
room MATH 126
The eighth moments of Dirichlet L-functions
room MATH 126
Thu 14 Mar 2013, 3:00pm-3:50pm

Abstract

Assuming GRH, I will give a proof for the asymptotic formula of the eighth moment of Dirichlet L-functions averaged over primitive characters χ modulo q, over moduli q<Q, with a short average in the t-aspect. We obtain the constant 24,024 as a factor in the leading-order term of the eighth moment, which is as predicted for the eighth moment of the Riemann zeta function. This talk is based on joint work with Xiannan Li.

Note for Attendees

Refreshments will be served between the two talks.
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University of Illinois, Urbana-Champaign
Thu 14 Mar 2013, 4:10pm
Number Theory Seminar
room MATH 126
The Riemann zeta function on arithmetic progressions
room MATH 126
Thu 14 Mar 2013, 4:10pm-5:00pm

Abstract

I will talk about the distribution of the values of the zeta function on points lying in an arithmetic progressions on the critical line. This research was originally motivated by questions about the primes and the linear independence conjecture. We discover some interesting correlations between such distributions along sparse discrete points and the usual distribution of values on the entire critical line. Among other applications, this allows us to prove that a positive proportion of such points are not zeros of zeta, improving a previous result of Martin and Ng. (based on joint work with M. Radziwill)
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Robert Fraser
UBC
Mon 18 Mar 2013, 3:00pm
Harmonic Analysis Seminar
Math 126
Embedding triangles in the primes
Math 126
Mon 18 Mar 2013, 3:00pm-4:00pm

Abstract

A common type of problem in additive number theory involves estimating the number of solutions to a system of Diophantine equations among the primes. We estimate the number of ways to embed a similar copy of a given triangle T in the primes by applying the Hardy-Littlewood circle method to count the number of prime solutions a system of quadratic Diophantine equations depending on the triangle T. The number of \log -weighted solutions to the system for which each coordinate is at most N is shown to be asymptotic to a constant depending on the singular series times N^{2n-4}, where n \geq 7 is the number of dimensions.
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New York University
Mon 18 Mar 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB Rm 4127, (PIMS video conference room). Note the date, time and place change.
Scattering for nonlinear dispersive equations in the presence of a potential
ESB Rm 4127, (PIMS video conference room). Note the date, time and place change.
Mon 18 Mar 2013, 3:30pm-4:30pm

Abstract

Questions related to the asymptotic behavior of nonlinear dispersive equations in the presence of a potential term are of great interest both for mathematical and physical reasons. Our main concern will be equations with low-degree nonlinearities, namely below the Strauss exponent threshold, for which classical energy and decay methods fail to suffice. For this, we we use the spectral theory of the operator H=-\Delta+V to develop a space-time resonance analysis adapted to the inhomogeneous setting. A key ingredient in this setup is the development of a sufficiently comprehensive multilinear harmonic analysis in the context of the corresponding distorted Fourier transform. This turns out to exhibit several intriguing differences in comparison to the unperturbed Euclidean setting (no matter how small V is). As a first application, we treat the case of a quadratic nonlinear Schrodinger equation on \R^3.

This is joint work with Pierre Germain and Samuel Walsh (Courant Institute, NYU).
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Georgia Tech
Tue 19 Mar 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
The Stability of Cylindrical Pendant Drops
ESB 2012 (in the new PIMS building)
Tue 19 Mar 2013, 3:30pm-4:30pm

Abstract

  In 1980 Henry Wente considered the variational stability of rotationally symmetric pendant drops and obtained a number of results for various problems.

We consider one version of one of those problems for cylindrical pendant drops trapped between parallel planes.  The analysis is different in various ways, and leads to results of a different nature.  Most notably, Wente's rotationally symmetric pendant drops form stable families which terminate at a maximum volume. We find stable families which terminate at a maximum volume, but are followed by (distinct disconnected) families of stable drops. As a result, we may have "large" stable pendant drops which become unstable and "drip" when the volume is decreased.

We will attempt to explain these results using the simpler zero gravity case as a model.
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Steve Bennoun
Wed 20 Mar 2013, 12:30pm SPECIAL
One Time Event
Graduate Student Center, Room 203
Doctoral Exam
Graduate Student Center, Room 203
Wed 20 Mar 2013, 12:30pm-3:00pm

Details

Consider a weak bialgebra H, is it possible to invert some elements and still have a weak bialgebra structure? If so, is there conditions on H or on the set of elements we want to invert? We thoroughly investigate these questions and establish sufficient conditions for the localization of a weak bialgebra to exist. We show that a monoid of group-like elements that is almost central, a condition we introduce here, forms a suitable set to be localized.
We give constructive proofs of these results and then use them to produce interesting examples of bialgebras and weak bialgebras.
We also present a reformulation of Manin's Hopf envelope and use it to define the notion of weak Hopf envelope. We finally discuss the relationship between the localization of a weak bialgebra relative to the monoid of all group-like elements and the weak Hopf envelope.
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Stanford University
Wed 20 Mar 2013, 3:00pm
Topology and related seminars
ESB 4127
Stability in the unstable cohomology of mapping class groups, SL_n(Z), and Aut(F_n)
ESB 4127
Wed 20 Mar 2013, 3:00pm-4:00pm

Abstract

For each of the sequences of groups in the title, the k-th rational cohomology is independent of n in a linear range n >= c*k, and this "stable cohomology" has been explicitly computed in each case. In contrast, very little is known about the unstable cohomology, which lies outside this range.

I will explain a conjecture on a new kind of stability in the unstable cohomology of these groups, in a range near the "top dimension" (the virtual cohomological dimension). For SL_n(Z) the conjecture implies that the unstable cohomology actually vanishes in that range. One key ingredient is a version of Poincare duality for these groups based on the topology of the curve complex and the algebra of modular symbols. Based on joint work with Benson Farb and Andrew Putman.
 

 

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Laura Peskin
California Institute of Technology
Thu 21 Mar 2013, 3:00pm
Number Theory Seminar
room MATH 126
Mod p representations of the metaplectic cover of SL_2(Q_p), via Hecke algebras
room MATH 126
Thu 21 Mar 2013, 3:00pm-3:50pm

Abstract

The local Shimura correspondence relates representations of PGL2 to those of the metaplectic cover of SL2, where both groups are p-adic and the representations are on C-vector spaces. Many pieces of the usual construction break down, due to non-semisimplicity, when the representations are instead taken over a field of positive characteristic. The mod p case is especially problematic. In the specific case of the pair (\tilde{SL}2, PGL2), I will discuss an alternate approach using a comparison of certain Hecke algebras of each group. The focus will be on the nonsupercuspical representations; I'll classify these for the cover of SL2, and relate them to the genuine spherical and Iwahori Hecke algebras. 

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 21 Mar 2013, 4:10pm
Number Theory Seminar
room MATH 126
Ternary quadratic forms and half-integral weight modular forms
room MATH 126
Thu 21 Mar 2013, 4:10pm-5:00pm

Abstract

Let k be a positive integer that is congruent to 3 (mod 4), and let N be a positive square-free integer. In this talk, we show how to compute a basis for the two-dimensional subspace Sk/20(4N),F) of half-integral weight modular forms associated, via the Shimura correspondence, to a newform in Sk-10(N)), which satisfies L(F,1/2) ≠ 0. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given F via local considerations, once a form in the Kohnen space has been determined.
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Stanford
Fri 22 Mar 2013, 3:00pm
Department Colloquium
MATX 1100
Combinatorial stability and representation stability
MATX 1100
Fri 22 Mar 2013, 3:00pm-4:00pm

Abstract

 If you choose a squarefree polynomial f(T) in F_q[T] uniformly at random, it will have slightly less than one linear factor on average; as deg f(T) goes to infinity, this expectation stabilizes and converges to 1 - 1/q + 1/q^2 - 1/q^3 + ... = q / (q+1). In joint work with J. Ellenberg and B. Farb, we proved that the stabilization of this combinatorial formula, and other statistics like it, is equivalent to a representation-theoretic stability in the cohomology of braid groups. I will describe how combinatorial stability for statistics of squarefree polynomials, of tori in GL_n(F_q), and other natural geometric counting problems can be converted to questions of representation stability in topology, and vice versa.
 
This talk will assume no background, and is intended for a general mathematical audience.

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University of Surrey, Guildford
Mon 25 Mar 2013, 3:00pm
Harmonic Analysis Seminar
Math 126
Intersection properties of random measures, and applications
Math 126
Mon 25 Mar 2013, 3:00pm-4:00pm

Abstract

The last few years saw an explosion of interest in understanding the geometry of the projections and slices of random fractals (such as fractal percolation). We develop a framework that allows us to recover, improve and unify many of  these results, for a large class of random measures (essentially Kahane's T-Martingales with an additional spatial independence assumption).

Our results have several applications, of which I will focus on two: sharp dimension results for tube-null sets, and the presence of patterns such as progressions, angles or distances in random fractals. These applications are motivated by problems in harmonic analysis and geometric measure theory.

This is joint work with V. Suomala.

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University of Oregon
Mon 25 Mar 2013, 3:10pm
Algebraic Geometry Seminar
ESB 2012
The Combinatorial PT-DT correspondence
ESB 2012
Mon 25 Mar 2013, 3:10pm-4:10pm

Abstract

I will discuss a combinatorial problem which comes from algebraic geometry. The problem, loosely, is to show that two theories for "counting" "curves" (Pandharipande-Thomas theory and reduced Donaldson-Thomas theory) give the same answer. I will prove a combinatorial version of this correspondence in a special case (X is toric Calabi-Yau), where the difficult geometry reduces to a study of the "topological vertex'' (a certain generating function) in these two theories. The combinatorial objects in question are plane partitions, perfect matchings on the honeycomb lattice and the double dimer model.

There will be many pictures. This is a combinatorics talk, so no algebraic geometry will be used, except as an oracle for predicting the answer.
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Maryam Fazel
Electrical Engineering, University of Washington
Tue 26 Mar 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Recovery and Denoising for Simultaneously Structured Models
ESB 4133
Tue 26 Mar 2013, 12:30pm-1:30pm

Abstract

We consider models or signals with simultaneous structure, for example a matrix that is simultaneously sparse and low-rank. Our goal is to find suitable convex penalties that allow us to reconstruct such signals given random measurements and noisy observations. 
 
Often penalties that promote each individual structure are known and yield an order-wise optimal number of measurements (e.g., \ell 1 norm for sparsity, nuclear norm for matrix rank), so it is reasonable to minimize a combination of such norms. We show that, surprisingly, if we use multi-objective optimization with the individual norms, then we can do no better (order-wise) in terms of required measurements than an algorithm that exploits only one of the structures. This result suggests that to fully exploit the multiple structures, we need an entirely new convex relaxation, not one that is a function of convex relaxations used for each structures.
 
Bio: Maryam Fazel is an assistant professor in Electrical Engineering at the University of Washington since 2008. She received her MS and PhD in EE from Stanford University and her BS in EE from Sharif University in Iran, and was a Postdoctoral Scholar at Caltech prior to joining UW. Maryam is a recipient of the NSF Career Award (2009), and the UW EE Outstanding Teaching Award (2009).
 

Note for Attendees

Pizza and pop refreshments.
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UCLA
Tue 26 Mar 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
Quasi-static evolution in randomly perforated media
ESB 2012 (in the new PIMS building)
Tue 26 Mar 2013, 3:30pm-4:30pm

Abstract

We consider a quasi-static free boundary problem (the Hele-Shaw problem) in a randomly perforated domain with zero Neumann boundary conditions. A homogenization limit is obtained as the characteristic scale of the domain goes to zero. Specifically, we prove that the solutions as well as their free boundaries converge uniformly to those corresponding to a homogeneous and anisotropic Hele-Shaw problem set in $\mathbb{R}^d$.  This is joint work with Nestor Guillen.


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Daniel Brian Krupp
Queen’s University
Wed 27 Mar 2013, 12:00pm
Mathematical Education
MATH 126
Lunch series on Teaching and Learning: Cooperation and competition in the classroom
MATH 126
Wed 27 Mar 2013, 12:00pm-1:00pm

Abstract

The classroom is a microcosm of the human social universe. In it, there are numerous opportunities for cooperation and for competition—over marks, reputation, status, alliances, and mates. How the tension between cooperation and competition is resolved both in and outside of the classroom may be dictated in part by the structural demands of the educational system (e.g. the distribution of competition in space) as well as information about the value of education arising from external sources (e.g. cues of life expectancy). Here, I present new research on the possible effects of these informational and structural demands on measures of personal “investment” in education: educational attainment, graduation rates, school attendance, and course performance. Following this, I discuss avenues for future investigation.
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UBC
Thu 28 Mar 2013, 2:00pm
Algebraic Groups and Related Structures
Math 126
Pseudo-reflection groups and essential dimension.
Math 126
Thu 28 Mar 2013, 2:00pm-3:00pm

Abstract

An n x n complex matrix is called pseudo-reflection if its eigenvalues are 1, ..., 1. t, where t \ne 1 is a root of unity. Finite groups generated by pseudo-reflections were classified by Shephard and Todd in the 1950s. This classification is one of the high points of invariant theory of finite groups. Research into the various aspects of the structure of pseudo-reflection groups continues to this day. In this talk, based on joint work with A. Duncan, I will present a simple formula for the local essential dimension of a pseudo-reflection group. I will also discuss global essential dimension and a related intermediate notion between local and global. Some of these results can be restated in purely representation-theoretic terms, without any reference to essential dimension.
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Brian Marcus
UBC
Thu 28 Mar 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Factor Graphs, Belief Propagation II
Math Annex 1102
Thu 28 Mar 2013, 2:30pm-4:00pm

Abstract


Continuation of talk on March 14.

This is part of the informal learning seminar on Information, Physics and Computation
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Boston College
Thu 28 Mar 2013, 3:30pm
Number Theory Seminar
room MATH 126
A higher weight Gross-Zagier theorem
room MATH 126
Thu 28 Mar 2013, 3:30pm-4:30pm

Abstract

For a weight two modular form f, the Gross-Zagier theorem is a formula relating two things: the central derivative of the convolution L-function of f with a weight-one theta series, and the Neron-Tate pairing of a Heegner point with itself. I'll discuss a generalization to higher weight modular forms, where the Heegner point is replaced by certain special cycles on a unitary Shimura variety. This is joint work with Jan Bruinier and Tonghai Yang.
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