UBC

Tue 4 Sep 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105 [The NEW LOCATION!]

The Dyson Game (joint work with R. Carmona and M. Cerenzia)

MATH 105 [The NEW LOCATION!]
Tue 4 Sep 2018, 3:30pm4:30pm
Abstract
The Dyson game is an explicitly solvable N player dynamic game that admits Dyson Brownian motion as a Nash equilibrium. The game is motivated by the real world phenomenon found in the spacing of buses, parked cars and perched birds, which exhibit random matrix statistics (i.e. Dyson Brownian motion). We find the optimal repulsion parameter (universality class) of the equilibrium depends on the information available to the players, furthering the understanding of an open problem in random matrix theory proposed by Deift. The limiting mean field game has a local cost term, which depends on the optimal universality class due to the nontrivial asymptotic behavior of the players. We solve the mean field game master equation and the associated HamiltonJacobi equation on Wasserstein space exactly, and we discuss how generalizing our results will require answering novel questions on the analysis of these equations on infinite dimensional spaces.
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Tue 4 Sep 2018, 4:30pm
SPECIAL
MATH 125

Department Graduate Orientation

MATH 125
Tue 4 Sep 2018, 4:30pm6:00pm
Details
Refreshments available.
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University of Washington

Wed 5 Sep 2018, 2:45pm
Topology and related seminars
ESB 4133 (PIMS)

Coalgebra and Comodule Structure on Derived Quotients in infinitycategories

ESB 4133 (PIMS)
Wed 5 Sep 2018, 2:45pm3:45pm
Abstract
Any cobordism spectrum M associated to a classifying space BG is naturally equipped with a socalled Thom diagonal M>M ^ BG+ and Thom isomorphism M ^ M > M ^ BG+ . In the homotopy category, these maps give M the structure of a cotorsor for the coalgebra BG+. I'll describe how this structure can be lifted to the derived setting by proving a more general theorem about derived or "stacky" quotients of Enrings in ∞categories. This theorem states that, given an action by an nfold loop space G on an Enring R, the stacky or derived quotient R//G is naturally a BG+cotorsor (the fact that this specializes to a result for cobordism spectra follows from the work of Ando, Blumberg, Gepner, Hopkins and Rezk on Thom spectra and orientations). This result can be reinterpreted in the setting of noncommutative spectral algebraic geometry as saying that Spec(R//G) is a principal Spec(BG+)bundle (or torsor) over Spec(R) in the category of affine Envarieties. If there is time, I'll speculate wildly about applications to geometry and noncommutative algebra.
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Imperial College London

Mon 10 Sep 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

Four dimensional Fano quiver flag zero loci

MATH 126
Mon 10 Sep 2018, 4:00pm5:00pm
Abstract
The classification of Fano varieties is unknown beyond dimension 3; however, many Fano fourfolds are expected to be GIT theoretic subvarieties of either toric varieties or quiver flag varieties. Quiver flag varieties are a generalization of type A flag varieties and are GIT quotients of vector spaces. In this talk, I will discuss my recent work on quiver flag varieties, including a proof of the Abelian/nonAbelian correspondence for quiver flag varieties, and its application in the large scale computer search for Fano fourfolds that I have carried out in joint work with T. Coates and A. Kasprzyk. We find 139 new Fano fourfolds. I will also discuss the importance of these subvarieties as a testing ground for the conjectures of Coates, Corti, Galkin, Golyshev, Kasprzyk and Tveiten on mirror symmetry for Fano varieties.
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Utah State University

Tue 11 Sep 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Superposition Formulas for Differential Systems and Darboux Integrability

MATH 105
Tue 11 Sep 2018, 3:30pm4:30pm
Abstract
The quintessential example of a Darboux integrable differential equation is the Liouville equation
u_{xy} = 2 {\rm e}^u,
whose general solution is given by
u= \log \frac{ f'(x) g'(y)}{(f(x)g(y))^2}.
Daboux integrability is classically related to the existence of intermediate integrals (or Riemann invariants) which in turn allow an explicit closed form formula to be derived for these equations.
Motivated by work of E. Vessiot, I will describe a differential geometric construction which provides a fundamental description of Darboux integrable systems in terms of superposition of differential systems and the quotient theory of differential systems by Lie groups.
The general theory will be discussed (I won't assume familiarity with differential systems), and demonstrated with examples. If time permits some interesting properties of these systems will be shown based on the existence of the quotient representation of Darboux integrable systems.
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Indiana University

Wed 12 Sep 2018, 2:45pm
Topology and related seminars
ESB 4133 (PIMS)

Khovanov homology via immersed curves in the 4punctured sphere

ESB 4133 (PIMS)
Wed 12 Sep 2018, 2:45pm3:45pm
Abstract
We will describe a geometric interpretation of Khovanov homology as Lagrangian Floer homology of two immersed curves in the 4punctured 2dimensional sphere. The main ingredient is a construction which translates Khovanov (or BarNatan) invariant of a 4ended tangle to an immersed curve. It is inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4ended reduced Khovanov arc algebra (or, equivalently, BarNatan dotted cobordism algebra) into the Fukaya category of the 4punctured sphere. The main tool we will use is a category of peculiar modules, introduced by Zibrowius, which is a model for the Fukaya category of 2sphere with 4 discs removed. This is joint work with Liam Watson and Claudius Zibrowius.
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Wed 12 Sep 2018, 3:45pm
SPECIAL
PIMS Lounge (ESB 4133), Earth Sciences Bldg.

PIMS Afternoon Tea

PIMS Lounge (ESB 4133), Earth Sciences Bldg.
Wed 12 Sep 2018, 3:45pm4:15pm
Details
The PIMS tea will be held on Wednesdays in term 1 starting September 12th.
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UCLA

Thu 13 Sep 2018, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATH 126

Hodge theory of classifying stacks

MATH 126
Thu 13 Sep 2018, 4:00pm5:00pm
Abstract
The goal of this talk is to create a correspondence between the representation theory of algebraic groups and the topology of Lie groups. The idea is to study the Hodge theory of the classifying stack of a reductive group over a field of characteristic p, the case of characteristic 0 having been studied by Behrend, Bott, Simpson and Teleman. The approach yields new calculations in representation theory, motivated by topology.
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UCLA

Fri 14 Sep 2018, 4:00pm
Department Colloquium
ESB 2012

Birational geometry and algebraic cycles

ESB 2012
Fri 14 Sep 2018, 4:00pm5:00pm
Abstract
A fundamental problem of algebraic geometry is to determine which algebraic varieties are rational, that is, isomorphic to projective space after removing lowerdimensional subvarieties from both sides. We discuss the history of the problem. Some dramatic progress in the past 5 years uses a new tool in this context: the Chow group of algebraic cycles.
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University of Waterloo

Mon 17 Sep 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

Interpolating between the BatyrevManin and Malle Conjectures

MATH 126
Mon 17 Sep 2018, 4:00pm5:00pm
Abstract
The BatyrevManin conjecture gives a prediction for the asymptotic growth rate of rational points on varieties over number fields when we order the points by height. The Malle conjecture predicts the asymptotic growth rate for number fields of degree d when they are ordered by discriminant. The two conjectures have the same form and it is natural to ask if they are, in fact, one and the same. We develop a theory of point counts on stacks and give a conjecture for their growth rate which specializes to the two aforementioned conjectures. This is joint work with Jordan Ellenberg and David ZureickBrown.
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Institute for Computational & Mathematical Engineering, Stanford University

Tue 18 Sep 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Implementing a Smooth Exactly Penalty Function for Nonlinear Optimization

ESB 4133 (PIMS Lounge)
Tue 18 Sep 2018, 12:30pm1:30pm
Abstract
We describe a penalty function for constrained nonlinear programs, originally proposed by Fletcher (1970). This penalty function is smooth and exact, so that minimizers of the original problem are minimizers of the penalty function for a sufficiently large (but finite) penalty parameter. The main computational kernel required to evaluate this penalty function and its derivatives is solving augmented leastsquares like systems. The penalty function can then be efficiently evaluated for problems where good preconditions exist, such as for PDEconstrained optimization problems. We discuss extensions to regularized problems, problems with inequality constraints, and the use of inexact evaluations. We provide some preliminary numerical results on some standard optimization test problems and PDEconstrained problems.
This is joint work with Michael Friedlander, Dominique Orban and Michael Saunders.
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UBC

Wed 19 Sep 2018, 2:50pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Representation theory and arithmetic statistics of generalized configuration spaces

ESB 4133 (PIMS Lounge)
Wed 19 Sep 2018, 2:50pm3:50pm
Abstract
ChurchEllenbergFarb introduced the theory of FImodules to explain the phenomenon of representation stability of the cohomology of configuration spaces. I will explain the basics of how this story goes, and then explain how to extend their analysis to two generalized types of configuration spaces. Furthermore, I will explain how the GrothendieckLefschetz formula connects these topological stability phenomena to stabilization of statistics for polynomials and rational maps over finite fields.
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UBC Okanagan

Wed 19 Sep 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127

Chronic Hepatitis B Virus and Liver Fibrosis: A Mathematical Model

ESB 4127
Wed 19 Sep 2018, 3:00pm3:45pm
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University of Massachusets

Mon 24 Sep 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

Knot invariants, Hilbert schemes and arc spaces

MATH 126
Mon 24 Sep 2018, 4:00pm5:00pm
Abstract
In my talk I will explain (partially conjectural) relation between
1) Homology of Hilbert scheme of points on singular curves
2) Knot homology of the links of curve singularities
3) Space functions on the moduli space of maps from the formal disc to the curve singularities.
I will center my talk around discussion of the case of cuspidal curve x^m=y^n and its singularity. In this case it is now known that 1) 2) and 3) are essentially equal. Talk is based on the joint projects with Gorsky, Rozansky, Rasmussen, Shende and Yun.
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Department of Mechanical Engineering, University of Canterbury

Tue 25 Sep 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Evolution of Solid Bodies due to Melting, Erosion and Deposition

ESB 4133 (PIMS Lounge)
Tue 25 Sep 2018, 12:30pm1:30pm
Abstract
Moving boundary problems are found in many contexts including coastlines and the seabed on the large scale to atherosclerosis and blood clotting on the micro scale. The coupling between the fluid flow and evolving solid bodies is an important consideration when modelling these problems. We have run numerical simulations for the melting front of ice for both interior and exterior flows; classical examples of the Stefan problem. We also modelled erosion and colloidal deposition problems which involved other constitutive equations. The terminal shape of an eroding cylinder in cross flow was a rounded triangular profile pointed upstream, which agreed well with experimental results. All of these problems require careful attention to deformation of the mesh at the interface, and we have developed a node shuffle algorithm for preserving mesh quality at these boundaries.
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UBC

Wed 26 Sep 2018, 2:50pm
Topology and related seminars
ESB 4133 (PIMS lounge)

Symmetries of the Heegaard Floer theory of 4ended tangles

ESB 4133 (PIMS lounge)
Wed 26 Sep 2018, 2:50pm3:45pm
Abstract
The Heegaard Floer theory of a 4ended tangle takes the form of
an immersed curve (with possibly nontrivial local system) on the
boundary of the tangle minus the tangle ends. The Heegaard Floer
homology of a link can be computed as the Lagrangian intersection
theory of the Heegaard Floer homologies of two 4ended tangles
obtained by splitting the link along an embedded 2sphere.
I will outline the construction of the tangle invariant, with
particular focus on the action of the mapping class group of the
4punctured sphere. I will then discuss the current state of
symmetry properties for this invariant in the light of the
mutation conjecture.
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University of Ottawa

Thu 27 Sep 2018, 2:00pm
Mathematical Biology Seminar
ESB 4133

Population dynamics in patchy landscapes

ESB 4133
Thu 27 Sep 2018, 2:00pm2:50pm
Abstract

Mathematical models for population dynamics have a long history in biomathematics. They are tools to explore the effects of birth and death, species interaction, landscape quality and spatial movement on the persistence, spread and spatial distribution of a species. One particular question is how spatial variation in landscape attributes affects the dynamics of populations, for example in the context of species invasions. A relatively recent approach to this question divides a landscape into "patches" and incorporates smallscale individual movement information to predict largescale population dynamics. In this talk, I will review several aspects of this growing body of literature. I will include empirical evidence, model derivation, basic model outcomes, analytical challenges and some future ideas. The talk is aimed at a general mathbio audience.

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UBC Math

Fri 28 Sep 2018, 4:00pm
Department Colloquium
ESB 2012

Integers in manybody quantum physics

ESB 2012
Fri 28 Sep 2018, 4:00pm5:00pm
Abstract
Although integers are ubiquitous in quantum physics, they have different mathematical origins. In this colloquium, I will give a glimpse of how integers arise as either topological invariants or as analytic indices, as is the case in the socalled quantum Hall effect. I will explain the difficulties arising in extending wellknown arguments when one relaxes the approximation that the particles effectively do not interact with each other in matter. Recent advances have made such realistic generalizations possible.
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Note for Attendees
The time of this seminar has changed. It now starts at 2:45, and precedes PIMS tea (which is now at a later time).