Mathematics Dept.
  Events
Robert Jerrard
University of Toronto
Tue 5 Jan 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012
Vortex filaments in the Euler equation
ESB2012
Tue 5 Jan 2016, 3:30pm-4:30pm

Abstract

 Abstract: Classical fluid dynamics arguments suggest that in certain
limits, the evolution of thin vortex filaments in an ideal incompressible
fluid should roughly be governed by an equation called the binormal
curvature flow. However, these classical arguments rely on assumptions
that are so unrealistic that it would be hard even to extract from them a
precise conjecture that admits any realistic possibility of a proof. We
present a different approach to this question that yields a reasonable
formulation of a conjecture and strong supporting evidence, and that
clarifies the very substantial obstacles to a full proof. Parts of the
talk are based on joint work with Didier Smets and with Christian Seis
 
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University of Kansas
Wed 6 Jan 2016, 3:00pm
Probability Seminar
ESB 2012
A monotone isomorphism theorem
ESB 2012
Wed 6 Jan 2016, 3:00pm-4:00pm

Abstract

In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary sequence to another that is coordinatewise smaller than or equal to the original sequence.
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MIT
Thu 7 Jan 2016, 3:30pm
Number Theory Seminar
room MATH 126
Equidistribution for cuspidal automorphic representations
room MATH 126
Thu 7 Jan 2016, 3:30pm-4:30pm

Abstract

Consider the set of Hecke eigenforms of a fixed weight k and very large level N, and pick a prime p coprime to N. How are the eigenvalues of the operator Tp distributed? We will relate this question to a more abstract question about the distribution of local components of cuspidal automorphic representations. For a (reductive) algebraic group G defined over a p-adic field L, there is a measure, called the 'Plancherel measure', which is expected to serve as the limiting distribution under many circumstances. We'll define this measure, give a precise formulation of the problem, and discuss progress in this area of research. No prior knowledge of reductive groups or automorphic forms will be assumed.
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Australian National University
Mon 11 Jan 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
The braid group, the free group, and 2-linearity
MATH 126
Mon 11 Jan 2016, 3:00pm-4:00pm

Abstract

The ADE braid group acts faithfully on the derived category of coherent sheaves on the resolution of the associated Kleinian singularity. In other words, the ADE braid groups are "2-linear" groups. In a similar spirit, the free group is a 2-linear group. In this talk we'll describe a few proofs of these results and explain how spherical twists and triangulated categories are related to some open problems in group theory.

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UBC Math
Tue 12 Jan 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
The singular mass of a domain and critical dimensions associated to the Hardy-Schrodinger operator
Tue 12 Jan 2016, 3:30pm-4:30pm

Abstract

I consider two different approaches for breaking scale invariance and restoring compactness for borderline variational problems involving the Hardy-Schrodinger operator -\Delta -\frac{\gamma}{|x|^2} on a domain containing the singularity 0, either in its interior or on its boundary. One consists of adding a linear perturbation, another exploits the geometry of the domain. I discuss the role of various ``positive singular mass theorems" that help account for the critical dimensions below which these approaches fail. This is a joint project with Frederic Robert.
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Université d'Angers
Wed 13 Jan 2016, 3:00pm
Probability Seminar
ESB 2012
On the exit time from a cone for random walks with drift
ESB 2012
Wed 13 Jan 2016, 3:00pm-4:00pm

Abstract

The counting of walks in orthants is now a classical domain in enumerative combinatorics. In this talk, I will focus my attention on the growth constant for the number of such walks and show how the general framework of random walks in cones provides - via classical probabilistic tools - a unified solution to the problem of determining this growth constant. Joint work with Kilian Raschel.

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Alejandro Adem
University of British Columbia
Wed 13 Jan 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Homotopy Group Actions I
ESB 4133 (PIMS Lounge)
Wed 13 Jan 2016, 3:15pm-4:15pm

Abstract

In these talks we review basic facts about finite group actions and how they can be extended using homotopical methods. In the second talk we will describe some joint work with J.Grodal on constructing exotic group actions for certain rank two finite groups.
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UBC
Thu 14 Jan 2016, 3:30pm
Number Theory Seminar
room MATH 126
Simultaneous torsion points in a Weierstrass family of elliptic curves
room MATH 126
Thu 14 Jan 2016, 3:30pm-4:30pm

Abstract

In 2010, Masser and Zannier proved that there are at most finitely many complex λ not equaling 0 or 1, such that two points on the Legendre elliptic curve y2=x(x−1)(x−λ) with x-coordinates 2 and 3 are simultaneously torsion. Recently, Stoll proved that there is in fact no such λ, and it is his result that inspires our work. In this talk we will focus on the Weierstrass family of elliptic curves y2=x3+λ, and show that in many instances there will be no parameter λ such that the points (a,*) and (b,*) are simultaneously torsion. In contrast to the original approach of Masser and Zannier, we will place this problem in the setting of arithmetic dynamics, by studying whether a and b are simultaneously preperiodic for a Lattes map. The results in this talk are obtained by analyzing the 2-adic behaviour of the iterates of the Lattes map.
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University of Iowa
Fri 15 Jan 2016, 3:00pm
Department Colloquium
Math Annex 1100
From Operator Algebra to Free Function Theory
Math Annex 1100
Fri 15 Jan 2016, 3:00pm-4:00pm

Abstract

In the summer of 1966, when I was taking a reading course from Paul Halmos, he told me: "If you want to study a question about operators on infinite dimensional Hilbert spaces, first formulate it in the setting of finite dimensional spaces. Answer it there, and only then move on to the infinite dimensional setting." While this admonition may seem naive, I want to show how taking it seriously can reveal interesting connections between operator algebra and the theory of analytic functions of noncommutative variables. Very briefly: The journey begins with the work of Murray and von Neumann on rings of operators. Much of their inspiration came from finite group representation theory, and the algebras they constructed are viewed by many as infinite dimensional versions of semisimple algebras. When trying to fit non-semisimple algebras into operator algebra, Baruch Solel and I were inspired by algebraic theories developed in the late 40s and were led to think about tensor algebras and the theory of quivers (i.e., finite directed graphs). The algebras we constructed could profitably be studied as spaces of analytic functions on the algebras' representations. These are the free functions to which the title refers. The presentation will be largely historical and non-technical. It will require background only from first-year graduate courses in algebra and analysis.
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UBC
Mon 18 Jan 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
K-theoretic geometric Satake
MATH 126
Mon 18 Jan 2016, 3:00pm-4:00pm

Abstract

The geometric Satake equivalence relates the category of perverse sheaves on the affine Grassmannian and the representation category of a semisimple group G. We will discuss a quantum K-theoretic version of this equivalence. In this setup the representation category of G is replaced with (a quantum version) of coherent sheaves on G/G. This is joint work Joel Kamnitzer.

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Wed 20 Jan 2016, 10:00am
Math Education Research Reading
Math 126
"Flipping the calculus classroom: an evaluative study"
Math 126
Wed 20 Jan 2016, 10:00am-11:00am

Abstract


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University of Colorado Boulder
Wed 20 Jan 2016, 3:00pm
Probability Seminar
ESB 2012
Conditional Speed of BBM, Skeleton Decomposition and Application to Random Obstacles
ESB 2012
Wed 20 Jan 2016, 3:00pm-4:00pm

Abstract

 We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of $Z$ hits a trap,
asymptotically in time $t$. This proves to be a rich problem motivating the proof of
a more general result about the speed of branching Brownian motion conditioned on
non-extinction. We provide an appropriate ``skeleton" decomposition for the underlying
Galton-Watson process when supercritical and show that the ``doomed" particles do not contribute to the asymptotic decay rate.

This is joint work with M. Caglar and M. Oz (Istanbul); to appear in AIHP.
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Alejandro Adem
University of British Columbia
Wed 20 Jan 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Homotopy Group Actions II
ESB 4133 (PIMS Lounge)
Wed 20 Jan 2016, 3:15pm-4:15pm

Abstract

In these talks we review basic facts about finite group actions and how they can be extended using homotopical methods. In the second talk we will describe some joint work with J.Grodal on constructing exotic group actions for certain rank two finite groups.
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UBC
Fri 22 Jan 2016, 1:00pm
Graduate Student Seminar
Math 225
The Trouble with Transfinity
Math 225
Fri 22 Jan 2016, 1:00pm-2:00pm

Abstract

 We take a look at two extremely counterintuitive results in mathematics which are consequences of the existence of infinite sets, one of which explicitly invokes the axiom of choice, and the other more subtly. One is Goodstein's theorem, the other might be called the "Prisoners with hats" problem. This talk should be accessible to anyone with an understanding of sets, posets, and equivalence relations.

Note for Attendees

 Pizza and pop will be provided.
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Jae-Suk Park
POSTECH
Mon 25 Jan 2016, 3:00pm
Algebraic Geometry Seminar / Probability Seminar
MATH 126
Homotopy Theory of Probability Spaces
MATH 126
Mon 25 Jan 2016, 3:00pm-4:00pm

Abstract

The notion of a homotopy probability space is an enrichment of the notion of an algebraic probability space with ideas from algebraic homotopy theory. This enrichment uses a characterization of the laws of random variables in a probability space in terms of symmetries of the expectation. The laws of random variables are reinterpreted as invariants of the homotopy types of infinity morphisms between certain homotopy algebras. The relevant category of homotopy algebras is determined by the appropriate notion of independence for the underlying probability theory. This theory will be both a natural generalization and an effective computational tool for the study of classical algebraic probability spaces, while keeping the same central limit. 

This talk is focused on the commutative case, where the laws of random variables are also described in terms of certain affinely flat structures on the formal moduli space of a naturally defined family attached to the given algebraic probability space, which the relevant category is the homotopy category of L_\infty-algebras. Time permitting, I will explain a example of homotopy probability space which law corresponds to variations Hodge structures on a toric hypersurface.
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Professor of Mathematics, SFU
Tue 26 Jan 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Localized activation and intramuscular fat in muscle: an investigation using DG methods
ESB 4133 (PIMS Lounge)
Tue 26 Jan 2016, 12:30pm-1:30pm

Abstract


The response of the muscle-tissue unit (MTU) to activation and applied forces is affected by the architectural details as well as the material properties of this nearly-incompressible tissue. We will describe the (highly nonlinear) elastic equations governing this response for a fully three-dimensional, quasi-static, fully nonlinear and anisotropic MTU. We describe a three-field formulation for this problem, and present a DG discretization strategy. The scheme was implemented using {\tt deal.ii}. We present computational results about the effects of localized activation as well as the effects of fatty tissue on muscle response. This is joint with Sebastian Dominguez, Hadi Rahemi, David Ryan and James Wakeling.

Note for Attendees

Sushi lunch will be provided. We look forward to see you there.
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Wed 27 Jan 2016, 10:00am
Math Education Research Reading
Math 126
"A Study Of Students' readiness to Learn Calculus" by Carlson, Madison and West
Math 126
Wed 27 Jan 2016, 10:00am-11:00am

Abstract

 
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UBC Math
Wed 27 Jan 2016, 3:00pm
Probability Seminar
ESB 2012
Interlacements, Uniform Spanning Forests and the Aldous-Broder Algorithm.
ESB 2012
Wed 27 Jan 2016, 3:00pm-4:00pm

Abstract

 In the 1980’s, Aldous and Broder independently proved that the collection of first-entry edges of a random on a finite graph is distributed as a uniform spanning tree of the graph; using this fact to sample the uniform spanning tree of a finite graph is known as the Aldous-Broder algorithm.  In this talk, I will review the theorem of Aldous and Broder and discuss an extension of the Aldous-Broder algorithm to infinite graphs, in which the random walk is replaced by Sznitman’s random interlacement process. Time permitting, I will also show how this extension can be used to prove a few things about the wired uniform spanning forest. 
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Henrik Rüping
University of British Columbia
Wed 27 Jan 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Controlled Algebra
ESB 4133 (PIMS Lounge)
Wed 27 Jan 2016, 3:15pm-4:15pm

Abstract

In this talk I will give a introduction in a very useful tool – Controlled Algebra.

Controlled Algebra is a way of building new additive categories with better properties out of given ones. One application is the Definition of negative K-theory. Another application is a description of K-theoretic assembly maps as maps induced by additive functors.

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University of Ottawa
Thu 28 Jan 2016, 3:30pm
Number Theory Seminar
MATH 126
Howe-Kirillov's orbit method and faithful representation of finite p-groups
MATH 126
Thu 28 Jan 2016, 3:30pm-4:30pm

Abstract

A recent result of Karpenko and Merkurjev states that the essential dimension of a p-group G over a field K containing a primitive p'th root of unity is equal to the minimal dimension of faithful representations of G over K. Motivated by this result, it is then interesting to compute the minimal dimension of complex faithful representations of a given finite p-group. In this talk we will show how Lie algebraic method, namely Howe-Kirillov's orbit method, can be applied to answer this question for some classes of p-groups.
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