Stanford

Thu 5 Jan 2017, 4:00pm
SPECIAL
Probability Seminar
ESB 2012

Persistence of Gaussian stationary processes

ESB 2012
Thu 5 Jan 2017, 4:00pm5:00pm
Abstract
Consider a real Gaussian stationary process, either on Z or on R. That is, a stochastic process, invariant under translations, whose finite marginals are centred multivariate Gaussians. The persistence of such a process on [0,T] is the probability that it remains positive throughout this interval.
The relation between the decay of the persistence as T tends to infinity and the covariance function of the process has been investigated since the 1950s with motivations stemming from probability, engineering and mathematical physics. Nonetheless, until recently, good estimates were known only for particular cases, or when the covariance kernel of the process is either nonnegative or summable.
In the talk we discuss a new spectral point of view on persistence which greatly simplifies its analysis. This is then used to obtain better bounds in a very general setting.
Joint work with Naomi Feldheim and Shahaf Nitzan.
hide

Stanford University

Fri 6 Jan 2017, 3:00pm
Department Colloquium
ESB 2012

Lattice models of magnetism: from magnets to antiferromagnets

ESB 2012
Fri 6 Jan 2017, 3:00pm4:00pm
Abstract
The Ising model, and its generalisation, the Potts model, are two classical graphcolouring models for magnetism and antiferromagnetism. Albeit their simple formulation, these models were instrumental in explaining many realworld magnetic phenomena and have found various applications in physics, biology and computer science.
While our understanding of these models as modeling magnets has been constantly improving since the early twentieth century, little progress was made in treatment of Potts antiferromagnets.
In the talk, after a historical introduction to magnets, antiferromagnets and their modeling, we will describe how application of modern combinatorial and probabilistic methods resulted in recent breakthroughs in the rigorous analysis of Potts antiferromagnets.
hide

Bonn

Mon 9 Jan 2017, 1:30pm
Harmonic Analysis Seminar
Math 126

Entangled multilinear forms and applications

Math 126
Mon 9 Jan 2017, 1:30pm2:30pm
Abstract
We discuss L^p estimates for some multilinear singular integral forms and their applications to sharp quantitative norm convergence of ergodic averages with respect to two commuting transformations, quantitative cancellation estimates for the simplex Hilbert transform, and a question on side lengths of corners in dense subsets of the Euclidean space.
hide

University of Illinois at Chicago

Mon 9 Jan 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102

MordellWeil Groups of Hitchin Systems

MATX 1102
Mon 9 Jan 2017, 3:00pm4:00pm
Abstract
In this talk, I will discuss work giving in many cases a complete description of the group of rational sections of the relative Jacobian of a linear system of curves on a surface. By specializing to the case of spectral curves, we are able to determine very explicitly the group of sections of the Hitchin fibration. We will also discuss work in progress to extend this work to principal GHiggs bundles for more general groups G.
hide

McGill University

Mon 9 Jan 2017, 3:00pm
Department Colloquium
ESB 2012

Random discrete structures: Phase transitions, scaling limits, and universality

ESB 2012
Mon 9 Jan 2017, 3:00pm4:00pm
Abstract
The aim of this talk is to give an overview of some recent results in two interconnected areas:
*a) **Random graphs, random trees, and complex networks: *The last decade of the 20th century saw significant growth in the availability of empirical data on networks, and their relevance in our daily lives. This stimulated activity in a multitude of fields to formulate and study models of network formation and dynamic processes on networks to understand realworld systems.
One major conjecture in probabilistic combinatorics, formulated by statistical physicists using nonrigorous arguments and enormous simulations in the early 2000s, is as follows: for a wide array of random graph models on n vertices and degree exponent \tau>3, typical distance both within maximal components in the critical regime as well as on the minimal spanning tree on the giant component in the supercritical regime scale like n^{\frac{\tau\wedge 4 3}{\tau\wedge 4 1}}. In other words, the degree exponent determines the universality class the random graph belongs to. The mathematical machinery available at the time was insufficient for providing a rigorous justification of this conjecture.
More generally, recent research has provided strong evidence to believe that several objects, including
(i) components under critical percolation,
(ii) the vacant set left by a random walk, and
(iii) the minimal spanning tree,
constructed on a wide class of random discrete structures converge, when viewed as metric measure spaces, to some random fractals in the GromovHausdorffProkhorov sense, and these limiting objects are universal under some general assumptions. We report on recent progress in proving these conjectures.
*b) Stochastic geometry:* In contrast, less precise results are known in the case of spatial systems. We discuss a recent result concerning the length of spatial minimal spanning trees that answers a question raised by Kesten and Lee in the 90's, the proof of which relies on a variation of Stein's method and a quantification of the classical BurtonKeane argument in percolation theory.
Based on joint work with Louigi AddarioBerry, Shankar Bhamidi, Nicolas Broutin, Sourav Chatterjee, Remco van der Hofstad, and Xuan Wang.
hide


Mon 9 Jan 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012


ESB 2012
Mon 9 Jan 2017, 3:30pm4:30pm
Abstract
hide

Colin Macdonald, Department of Mathematics, UBC

Tue 10 Jan 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Parallel highorder timestepping with revisionist integral deferred correction

ESB 4133 (PIMS Lounge)
Tue 10 Jan 2017, 12:30pm1:30pm
Abstract
RIDC (revisionist integral deferred correction) methods are a class of time integrators wellsuited to parallel computing. RIDC methods can achieve highorder accuracy in wallclock time comparable to forward Euler. The methods use a predictor and multiple corrector steps. Each corrector is lagged by one time step; the predictor and each of the correctors can then be computed in parallel. This presentation introduces RIDC methods and demonstrates their effectiveness on some test problems.
hide

McGill

Tue 10 Jan 2017, 4:00pm
SPECIAL
Probability Seminar
ESB 2012

Intrinsic geometry of critical discrete structures

ESB 2012
Tue 10 Jan 2017, 4:00pm5:00pm
Abstract
Motivated by the presence of empirical data on a wide array of realworld networks, there has been an explosion in the number of random graph models proposed to explain various phenomenon observed in realworld systems including power law degree distribution and small world phenomenon. A major general theme in this area, since the time of Erdos and Renyi, has been understanding the properties of components in the critical regime. In the past five years, significant progress has been made in establishing scaling limits of critical random graphs and various constructs on random graphs when they are viewed as metric measure spaces, and understanding the general universality principles underlying such scaling limits. Further, striking connections between these questions and some of the central models of stochastic coalescence, and random interlacements and vacant set left by random walks have emerged. In this talk, we survey some recent results in this area and discuss general methodology for proving such results.
hide

UBC Mathematics

Tue 10 Jan 2017, 5:00pm
SPECIAL
Coach House, Green College, UBC

What is a Probabilist?

Coach House, Green College, UBC
Tue 10 Jan 2017, 5:00pm6:30pm
Details
Everyone understands the statement: "The probability of rain tomorrow is .90, or 90%. For a probabilist, many questions have answers of this type. The problem is to find that number.
hide


Wed 11 Jan 2017, 2:45pm
SPECIAL
PIMS Lounge (ESB 4133)

PIMS Afternoon Tea (resumes for Term 2)

PIMS Lounge (ESB 4133)
Wed 11 Jan 2017, 2:45pm3:10pm
Details
The tea runs until Wednesday, April 5th, 2017.
hide

Microsoft Research

Thu 12 Jan 2017, 4:00pm
SPECIAL
Probability Seminar
ESB 2012

Highdimensional random geometric graphs

ESB 2012
Thu 12 Jan 2017, 4:00pm5:00pm
Abstract
I will talk about a random geometric graph model, where connections between vertices depend on distances between latent ddimensional labels. We are particularly interested in the highdimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from the ErdosRenyi model. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an informationtheoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we compute the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, Ronen Eldan, and Jacob Richey.
hide

Microsoft Research

Fri 13 Jan 2017, 3:00pm
Department Colloquium
ESB 2012

Statistical inference in networks and genomics

ESB 2012
Fri 13 Jan 2017, 3:00pm4:00pm
Abstract
From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas.
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are rootfinding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying highdimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a highdensity, durable, and easytomanipulate storage medium of digital data
hide

Brown

Mon 16 Jan 2017, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

Functional interpretation for transverse arches of human foot

ESB 2012
Mon 16 Jan 2017, 3:00pm4:00pm
Abstract
Fossil record indicates that the emergence of arches in human ancestral feet coincided with a transition from an arboreal to a terrestrial lifestyle. Propulsive forces exerted during walking and running load the foot under bending, which is distinct from those experienced during arboreal locomotion. I will present mathematical models with varying levels of detail to illustrate a simple function of the transverse arch. Just as we curve a dollar bill in the transverse direction to stiffen it while inserting it in a vending machine, the transverse arch of the human foot stiffens it for bending deformations. A fundamental interplay of geometry and mechanics underlies this stiffening  curvature couples the soft outofplane bending mode to the stiff inplane stretching deformation. In addition to presenting a functional interpretation of the transverse arch of the foot, this study also identifies a classification of flat feet based on the skeletal geometry and mechanics.
hide

San Francisco State University

Mon 16 Jan 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102

Double Ramification Cycles and Tautological Relations

MATX 1102
Mon 16 Jan 2017, 3:00pm4:00pm
Abstract
Tautological relations are certain equations in the Chow ring of the moduli space of curves. I will discuss a family of such relations, first conjectured by A. Pixton, that arises by studying moduli spaces of ramified covers of the projective line. These relations can be used to recover a number of wellknown facts about the moduli space of curves, as well as to generate very special equations known as topological recursion relations. This is joint work with various subsets of S. Grushevsky, F. Janda, X. Wang, and D. Zakharov.
hide

San Francisco State University

Mon 16 Jan 2017, 4:15pm
Algebraic Geometry Seminar
MATX 1102

GenusOne LandauGinzburg/CalabiYau Correspondence

MATX 1102
Mon 16 Jan 2017, 4:15pm5:15pm
Abstract
First suggested by Witten in the early 1990's, the LandauGinzburg/CalabiYau correspondence studies a relationship between spaces of maps from curves to the quintic 3fold (the CalabiYau side) and spaces of curves along with 5th roots of their canonical bundle (the LandauGinzburg side). The correspondence was put on a firm mathematical footing in 2008 when Chiodo and Ruan proved a precise statement for the case of genuszero curves, along with an explicit conjecture for the highergenus correspondence. In this talk, I will begin by describing the motivation and the mathematical formulation of the LG/CY correspondence, and I will report on recent work with Shuai Guo that verifies the highergenus correspondence in the case of genusone curves.
hide

Department of Mathematics, SFU

Tue 17 Jan 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Sparse polynomial approximation of highdimensional functions

ESB 4133 (PIMS Lounge)
Tue 17 Jan 2017, 12:30pm1:30pm
Abstract
Many problems in scientific computing require the approximation of smooth, highdimensional functions from limited amounts of data. For instance, a typical problem in uncertainty quantification involves identifying the parameter dependence of the output of a computational model. Complex physical systems involve models with multiple parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality
essentially prohibits collecting or processing sufficient data to approximate the unknown function using classical techniques.
In this talk, I will give an overview of the approximation of smooth, highdimensional functions using sparse polynomial expansions. I will focus on the application of techniques from compressed sensing to this problem, and discuss the extent to which such approaches overcome the curse of dimensionality. If time, I will also discuss several extensions, including dealing with corrupted and/or unstructured data, the effect of model error and incorporating additional information such as gradient data. I will also highlight several challenges and open problems.
This is joint work with Casie Bao, Simone Brugiapaglia and Yi Sui (SFU).
hide

Kseniya Garaschuk and Eric Cytrynbaum
University of the Fraser Valley and UBC

Tue 17 Jan 2017, 12:30pm
Lunch Series on Teaching & Learning
Irving K. Barber Learning Ctr Room 461

Collaborative exams in large university courses

Irving K. Barber Learning Ctr Room 461
Tue 17 Jan 2017, 12:30pm1:30pm
Abstract
As we use more and more group work in our classes, should we consider introducing it into our assessments? One model that has been used are socalled twostage assessments, where students first complete and turn in the questions individually and then, working in small groups, answer the same questions again. This technique was first introduced in the UBC Faculty of Science in 2009 and is now being used in at least 20 science courses.
In this session, we will discuss a study of feasibility and effectiveness of twostage quizzes as introduced into two mathematics courses at UBC with a total of 834 students. We examine both short and long term retention resulting from introducing group assessments, we analyze results of collaborative learning based on question type and group composition. Finally, we present student and instructor feedback as well as discuss future directions of implementation and research.
hide

UBC Math

Tue 17 Jan 2017, 4:00pm
SPECIAL
Probability Seminar
ESB 2012

Boundary Harnack principle for diffusions

ESB 2012
Tue 17 Jan 2017, 4:00pm5:00pm
Abstract
The boundary Harnack principle (BHP) is a fundamental tool to understand the behaviour of positive harmonic functions near the boundary of a domain. For instance, the BHP implies a concrete description of the Martin boundary of a domain in geometric terms. Other applications of BHP include Carleson estimate, Fatou's theorem, and heat kernel estimates for diffusions killed upon exiting a domain. In this talk, I will discuss a recent extension of BHP that provides new examples of diffusions satisfying BHP even in R^n.
This is joint work with Martin Barlow.
hide

UBC Math

Wed 18 Jan 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012 (note special day)

Stability of elliptic Harnack inequality

ESB 2012 (note special day)
Wed 18 Jan 2017, 3:00pm4:00pm
Abstract
Harnack inequalities have proved to be a powerful tool in PDE (regularity estimates), geometry (geometric flows) and probability (heat kernel estimates). In the early 1990s Grigor'yan and SaloffCoste gave a characterisation of the parabolic Harnack inequality (PHI). This characterisation implies that PHI is stable under perturbations (quasiisometries). In this talk, I will provide an introduction to Harnack inequalities and discuss the stability of elliptic Harnack inequality.
This is joint work with Martin Barlow.
hide

Columbia University

Thu 19 Jan 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
seminar has been cancelled.

CANCELLED: Scaling limits of open ASEP and ferromagnetic Glauber dynamics

seminar has been cancelled.
Thu 19 Jan 2017, 3:30pm4:30pm
Abstract
We discuss two recent scaling limit results for discrete dynamics converging to stochastic PDEs. The first is the asymmetric simple exclusion process in contact with sources and sinks at boundaries, called Open ASEP. We prove that under weakly asymmetric scaling the height function converges to the KPZ equation with Neumann boundary conditions. The second is the Glauber dynamics of the BlumeCapel model (a generalization of Ising model), in two dimensions with Kac potential. We prove that the averaged spin field converges to the stochastic quantization equations. The main purpose of this talk is to discuss the general issues one needs to address when passing from discrete to continuum, the common challenge in the proofs of such scaling limit theorems, and how we overcome these difficulties in the two specific models. (Based on joint works with Ivan Corwin and Hendrik Weber)
hide

Columbia University

Fri 20 Jan 2017, 3:00pm
Department Colloquium
seminar has been cancelled.

CANCELLED: Singular Stochastic Partial Differential Equations  How do they arise and what do they mean?

seminar has been cancelled.
Fri 20 Jan 2017, 3:00pm4:00pm
Abstract
Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
hide

Toronto

Mon 23 Jan 2017, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

Matrix regulation of stem cell fate

ESB 2012
Mon 23 Jan 2017, 3:00pm4:00pm
Abstract
Stem cell fate is regulated by cues from the cellular microenvironment, including biophysical and biochemical cues presented by the extracellular matrix. Matrix regulation of cell fate has broad implications from disease to regeneration. In this talk, I will discuss our work aimed at determining how biophysical and biochemical cues from the matrix act to drive the fate and function of mesenchymal stem cells. In particular, I will discuss how the pathological differentiation of heart valve progenitor cells is modulated by the extracellular matrix and how we are using microdevices to dissect how matrix mechanical and biochemical cues act in concert to regulate mesenchymal stem cell differentiation and tissue regeneration.
hide

Rennes / PIMS

Mon 23 Jan 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102

On Grothendieck rings in real geometry

MATX 1102
Mon 23 Jan 2017, 3:00pm4:00pm
Abstract
The study of Grothendieck rings of varieties in the context of real algebraic geometry has begun since the apparition of motivic integration. Several such rings are of interest, depending notably on the class of functions we are interested in. We will discuss recent progress in the cases of real algebraic varieties and of arcsymmetric sets.
hide

Max Planck Institute Bonn

Tue 24 Jan 2017, 3:00pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
MATH 126

Chiral differential operators and the curved betagamma system

MATH 126
Tue 24 Jan 2017, 3:00pm4:00pm
Abstract
Chiral differential operators (CDOs) are a vertex algebra analog of the associative algebra of differential operators. Originally introduced by mathematicians, Witten explained how CDOs arise as the perturbative part of the curved betagamma system with target X. I will describe recent work with Gorbounov and Williams in which we construct the BV quantization of this theory and use a combination of factorization algebras and formal geometry to recover CDOs. At the end, I hope to discuss how the techniques we developed apply to a broad class of nonlinear sigma models, including source manifolds of higher dimension.
hide

Center for Geometry and Physics/ Pohang Univ. of Sci. and Tech. Korea.

Tue 24 Jan 2017, 4:10pm
SPECIAL
MATH 1102 Topology/Algebra/Math Physics seminar [We will start at 4:10pm]

A quantization of the unipotent fundamental group

MATH 1102 Topology/Algebra/Math Physics seminar [We will start at 4:10pm]
Tue 24 Jan 2017, 4:10pm5:10pm
Details
We construct two homotopy functors from the category of homotopy commutative algebras to the category of prounipotent group and the category of completed commutative Hopf algebras such that
(1) the group is isomorphic to the pro unipotent fundamental group of smooth connected and based manifold (M,*) and
(2) the Hopf algebra is that of homotopy functionals defined by Chen’s iterated path integrals over closed and based loops on M
if the homotopy commutative algebra is quasiisomorphic to the algebra of differential forms on M.
These constructions can be quantized in appropriate sense after interpreting them as doing “classical field theory” such that the pro unipotent fundamental group is the structure in the space of all "classical expectations" and the completed Hopf algebra is the algebra of “classical observables”. The quantization involves a generalized deformation quantization of homotopy commutative algebra into topologically free homotopy associative algebra along the direction of compatible homotopy Lie algebra.
hide

UBC

Wed 25 Jan 2017, 1:45pm
Mathematical Biology Seminar
PIMS, ESB 4th floor

Multiscale modeling of vesicular release at neuronal synapses.

PIMS, ESB 4th floor
Wed 25 Jan 2017, 1:45pm2:45pm
Abstract
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. I will present in this talk a hybrid discretecontinuum model that takes into account both a stochastic regime governed by rare events and a continuous regime in the bulk, in the context of vesicular release at chemical synapses.
In a first part, I computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. This models the binding of calcium ions on the SNARE complex, a process that triggers vesicular release. Using this result, I developed a model to study how vesicles and calcium channels organization shape such process.
In a second part, I will present a model for the presynaptic terminal built using the results described above. This model was formulated in an initial stage as a reactiondiffusion problem in a confined microdomain, where Brownian particles have to bind to small target sites. I coarsegrained this model into a system of mass action equations coupled to a set of Markov equations, which allows to obtain analytical results and to realize fast stochastic simulations.
hide

Max Planck Institute Bonn

Wed 25 Jan 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012 (note special day)

From Feynman diagrams to commutative diagrams

ESB 2012 (note special day)
Wed 25 Jan 2017, 3:00pm4:00pm
Abstract
Factorization algebras are localtoglobal objects that play a role in quantum field theory akin to the role of sheaves in geometry: they conveniently organize complicated information. In the talk I will introduce this notion, give some concrete examples, and then explain how factorization algebras mediate between QFT and higher algebra. An important example will be ChernSimons theory; ongoing work with Costello and Francis recovers quantum groups with formal parameter by combining Koszul duality with Feynman diagrams.
hide

University of Chicago

Wed 25 Jan 2017, 4:15pm
SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)

Quantitative Nullcobordism and the (in)effectiveness of algebraic topology.

ESB 4133 (PIMS Lounge)
Wed 25 Jan 2017, 4:15pm5:15pm
Abstract
Topology is full of ineffective arguments constructing objects and equivalences by algebra.
One of the great early achievements of algebraic topology was the work of Thom, followed by Milnor and Wall, on cobordism theory, which describes when a compact smooth (oriented) manifold is the boundary of some compact manifold with boundary. This method is typical of the problems that arise in the use of algebraic methods and is an early example of one of the dominant philosophies of geometric topology. The question we study is to what extent the complexity of a manifold can be used to bound, when it exists, the minimum necessary complexity of something that it bounds.
The goal of this talk is to explain generally some of the issues of making topology less ineffective.
We shall show that there are polynomial size nullcobordisms in a suitable sense. This is joint work with Greg Chambers, Dominic Dotterer and Fedor Manin.
hide

University of Texas at Austin

Thu 26 Jan 2017, 3:30pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
MATH 102

Cluster Theory of the Coherent Satake Category

MATH 102
Thu 26 Jan 2017, 3:30pm5:00pm
Abstract
We discuss recent work showing that in type A_n the category of equivariant perverse coherent sheaves on the affine Grassmannian categorifies the cluster algebra associated to the BPS quiver of pure N=2 gauge theory. Physically, this can be understood as a statement about line operators in this theory, following ideas of GaiottoMooreNeitzke, Costello, and KapustinSaulina  in short, coherent IC sheaves are the precise algebrogeometric counterparts of Wilson't Hooft line operators. The proof relies on techniques developed by KangKashiwaraKimOh in the setting of KLR algebras. A key moral is that the appearance of cluster structures is in large part forced by the compatibility between chiral and tensor structures on the category in question (i.e. by formal features of holomorphictopological field theory). This is joint work with Sabin Cautis.
hide

University of Texas at Austin

Fri 27 Jan 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

Canonical Bases and Physical Mathematics

ESB 2012
Fri 27 Jan 2017, 3:00pm4:00pm
Abstract
The discovery of socalled canonical (or crystal) bases of quantum groups by Lusztig and Kashiwara was one of the major milestones of Lie theory during the past three decades. The larger theory of canonical bases that grew out of their work (and others') has continually revealed surprising connections to other areas of mathematics such as algebraic and symplectic geometry. In this talk we sample some of these connections, for example to the geometry of character varieties of surfaces, and explain how ideas from theoretical physics provide an organizing framework for many mathematically disparate results. A central role is played by the flexible combinatorial language of cluster algebras, which provides a useful lingua franca for the subject.
hide

Institute for Theoretical Physics, KU Leuven

Mon 30 Jan 2017, 3:00pm
Department Colloquium
ESB 2012

Adiabatic Theory: From Spinning Top to Gapped Matter

ESB 2012
Mon 30 Jan 2017, 3:00pm4:00pm
Abstract
Adiabatic theory studies dynamical systems featuring separation of motion into slow and fast components. When the system is driven these components start mixing. The basic premise of adiabatic theory is that this mixing is small for slow driving. Furthermore, the resulting driven motion is irreversible in the slow component but reversible in the fast component. In this talk, I first illustrate this phenomena on a spinning top and state the classical adiabatic theorem of quantum mechanics. Then, I will show extensions of the theory to abstract Banach spaces and stochastic equations, culminating with an adiabatic theorem for extended systems where the separation holds uniformly in the volume of the system. An important corollary of this theorem is a proof of the Kubo formula for gapped interacting systems.
hide

University of Washington

Mon 30 Jan 2017, 3:00pm
Algebraic Geometry Seminar
Math 126

Fiber Powers and Uniformity

Math 126
Mon 30 Jan 2017, 3:00pm4:00pm
Abstract
In 1997 Caporaso, Harris and Mazur, motivated by uniformity results in Diophantine Geometry, proposed a conjecture about fibered powers of families of varieties of general type. In particular they conjecture that, if X > B is a family whose general fiber is a variety of general type, then for large n, the nth fiber power of X over B dominates a variety of general type. The conjecture has been proved by Abramovich and used to deduce interesting results on the distribution of rational points on projective varieties. I will discuss recent work, joint with Kenny Ascher (Brown), generalizing this to pairs (X,D) of a projective scheme and a divisor, and the new challenges that arise when one tries to obtain analogous results for the distribution of integral points in quasi projective varieties.
hide

Institute for Theoretical Physics, KU Leuven

Tue 31 Jan 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On Products of Correlated Matrices Originating in the Statistical Structure of Quantum Mechanics

ESB 2012
Tue 31 Jan 2017, 3:30pm4:30pm
Abstract
Statistics of measurement outcomes in quantum mechanics is described by a map that associates a matrix to each possible measurement outcome. The probability of this outcome is then given by a trace of this matrix. Probability of a sequence of measurement outcomes is computed in the same way from a product of associated matrices. In this talk I will describe two results related to this setting. A theorem giving optimal conditions for uniqueness of the associated invariant measure on the projective sphere, and a theorem describing large deviation theory in the case when the matrices commute. The latter problem received lots of recent attention following experiments of S.~Haroche.
hide


Tue 31 Jan 2017, 4:00pm
ESB 4127

Talk practice

ESB 4127
Tue 31 Jan 2017, 4:00pm5:00pm
Details
hide

Note for Attendees
Tea and cookies will be served at 2:45 p.m.