Mathematics Dept.
  Events
Tel-Aviv University
Mon 16 Oct 2017, 3:00pm
Harmonic Analysis Seminar
GEOG 101
Interpolation sets and arithmetic progressions
GEOG 101
Mon 16 Oct 2017, 3:00pm-4:00pm

Abstract

Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier
coefficients satisfy f^(k)=c(k) for all k in K. In the talk I will discuss the relationship between the concept of IS and the existence of arbitrarily
long arithmetic progressions with specified lengths and step sizes in K. Multidimensional analogue and recent developments will also be considered.
Based on joint work with A. Olevskii.
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FU Berlin
Mon 16 Oct 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126
Infinitesimal qG-deformations of cyclic quotient singularities
MATH 126
Mon 16 Oct 2017, 4:00pm-5:00pm

Abstract

The subject of the talk is two-dimensional cyclic quotients, i.e. two-dimensional toric singularities. We introduce the classical work of Koll'ar/Shephard-Barron relating the components of their deformations and the so-called P-resolutions, we give several combinatorial descriptions of both gadgets, and we will focus on two special components among them - the Artin component allowing a simultaneous resolution and the qG-deformations preserving the Q-Gorenstein property. That is, it becomes important that several (or all) reflexive powers of the dualizing sheaf fit into the deformation as well. We will study this property in dependence on the exponent r. While the answers are already known for deformations over reduced base spaces (char = 0), we will now focus on the infinitesimal theory. (joint work with János Kollár)
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Bamdad Hosseini
Department of Mathematics, SFU
Tue 17 Oct 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Non-Gaussian priors in Bayesian inverse problems: from theory to applications
ESB 4133 (PIMS Lounge)
Tue 17 Oct 2017, 12:30pm-1:30pm

Abstract

Statistical and probabilistic methods are promising approaches to solving inverse problems - the process of recovering unknown parameters from indirect measurements.  Of these, the Bayesian methods provide a principled approach to incorporating our existing beliefs about the parameters (the prior model) and randomness in the data. These approaches are at the forefront of extensive current investigation. Overwhelmingly, Gaussian prior models are used in Bayesian inverse problems since they provide mathematically simple and computationally efficient formulations of important inverse problems. Unfortunately, these priors fail to capture a range of important properties including sparsity and natural constraints such as positivity, and so we are motivated to study non-Gaussian priors. In this talk we introduce the theory of well-posed Bayesian inverse problems with non-Gaussian priors in infinite dimensions. We show that the well-posedness of a Bayesian inverse problem relies on a balance between the growth rate of the forward map and the tail decay of the prior. Next, we turn our attention to a concrete application of non-Gaussian priors in recovery of sparse or compressible parameters. We construct new classes of prior measures based on the Gamma distribution and develop a Markov Chain Monte Carlo algorithm for exploring the posterior measures that arise from our compressible priors in infinite dimensions. 
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Yonsei University
Tue 17 Oct 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Global well-posedness and asymptotics of a type of Keller-Segel models coupled to fluid flow
ESB 2012
Tue 17 Oct 2017, 3:30pm-4:30pm

Abstract

We study chemotaxis equations coupled to the Navier-Stokes equations, which is a mathematical model describing the dynamics of oxygen, swimming bacteria (Bacillus subtilis) living in viscous incompressible fluids. It is, in general, not known if regular solutions with sufficiently smooth initial data exist globally in time or develop a singularity in a finite time. We discuss existence of regular solutions and asymptotics as well as temporal decays of solutions, under a certain type of conditions of parameters (chemotatic sensitivity and consumption rate) or initial data, as time tends to infinity.
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Technical University of Berlin
Wed 18 Oct 2017, 3:00pm
Probability Seminar
ESB 2012
Harnack inequality for degenerate balanced random walks
ESB 2012
Wed 18 Oct 2017, 3:00pm-4:00pm

Abstract


We consider an i.i.d. balanced environment omega(x,e)=omega(x,-e), genuinely d dimensional on the lattice and show that there exist a positive constant C and a random radius R(omega) with streched exponential tail such that every non negative omega harmonic function u on the ball B_{2r} of radius 2r>R(omega), we have max_{B_r} u <= C min_{B_r} u. Our proof relies on a quantitative quenched invariance principle for the corresponding random walk in  balanced random environment and a careful analysis of the directed percolation cluster. This result extends Martins Barlow's Harnack's inequality for i.i.d. bond percolation to the directed case. This is joint work with N. Berger, M. Cohen, and X. Guo.
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Cornell University
Wed 18 Oct 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Deriving zeta functions
ESB 4133 (PIMS Lounge)
Wed 18 Oct 2017, 3:15pm-4:15pm

Abstract

The local zeta function of a variety X over a finite field F_q is defined to be Z(X,t) = \exp\sum_{n > 0}\frac{|X(F_{q^n})|}{n}. This invariant depends only on the point counts of X over extensions of F_q. We discuss how Z(X,t) can be considered as a group homomorphism of K-groups and show how to lift it to a map between K-theory spectra.
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Aaron Berk
Mathematics, UBC
Fri 20 Oct 2017, 12:00pm
Graduate Student Seminar
MATH 203
From Hoeffding's inequality to PAC learning
MATH 203
Fri 20 Oct 2017, 12:00pm-1:00pm

Abstract

The efficacy of machine learning algorithms hinges on their ability to generalize from data (i.e., when does small training error guarantee small test error). However, the theory of generalizability remains largely unexplained, particularly for monstrous networks that achieve ground-breaking performance on complex tasks like image classification, language translation, or the game Go. The goal of this talk is to showcase how a simple yet elegant phenomenon in probability - concentration of measure - informs the formalization of "learning from data". By way of Hoeffding's inequality, we show how PAC learning uses concentration of measure to address the problem of generalizability in machine learning.

This talk will be accessible to all graduate students and post-docs who've heard the phrase "Markov inequality" at least once. I chose the subject matter because it contains elegant math that yields deep results in an equally elegant formalization of a high-level salient concept. This talk is related but tangential to the subject matter of the probability reading group this term (i.e., I'd be excited to discuss how these results might generalize to more exciting cases).
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Cambridge
Fri 20 Oct 2017, 3:00pm
Department Colloquium
ESB 2012
Universality for the dimer model
ESB 2012
Fri 20 Oct 2017, 3:00pm-4:00pm

Abstract

The dimer model on a finite bipartite graph is a uniformly chosen perfect matching, i.e., a set of edges which cover every vertex exactly once. It is a classical model of mathematical physics, going back to work of Kasteleyn and Temeperley/Fisher in the 1960s, with connections to many topics including determinantal processes, random matrix theory, algebraic combinatorics, discrete complex analysis, etc.

A central object for the dimer model is a notion of height function introduced by Thurston, which turns the dimer model into a random discrete surface. I will discuss a series of recent results with Benoit Laslier (Paris) and Gourab Ray (Victoria) where we establish the convergence of the height function to a scaling limit in a variety of situations. This includes simply connected domains of the plane with arbitrary linear boundary conditions for the height, in which case the limit is the Gaussian free field, and Temperleyan graphs drawn on Riemann surfaces. In all these cases the scaling limit is universal (i.e., independent of the details of the graph) and conformally invariant.

A key new idea in our approach is to exploit "imaginary geometry" couplings between the Gaussian free field and Schramm's celebrated SLE curves.

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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