University of Alberta at Edmonton

Wed 1 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

FeynmanKac formula for the stochastic heat equation driven by general Gaussian noises

ESB 2012
Wed 1 Nov 2017, 3:00pm4:00pm
Abstract
In this talk I will present some results on stochastic heat equations driven by a Gaussian noises. I will focus on FeynmanKac representation of the solution and the moments of the solution. Both lower and upper bounds for the L^p moments of the solution are obtained which is relevant to the socalled intermittency. The Driving Gaussian noises include fractional Brownian fields of Hurst parameters greater or smaller than 1/2.
hide

UBC

Wed 1 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133

Symmetric Powers and the Dual Steenrod Algebra  Part 2

ESB 4133
Wed 1 Nov 2017, 3:15pm4:15pm
Abstract
In episode 2 of the series, I will turn my attention to the setting of Gequivariant stable homotopy theory, where G is an abelian pgroup. Analogous to the classical case, we can use symmetric powers of the equivariant sphere to filter H\underline{\F}_p, and the cofibers are Steinberg summands of equivariant classifying spaces. We then study how the cells of these spaces split after smashing with H\underline{\F}_p in the case G=C_p. When p=2, the result is a decomposition of H\underline{\F}_2 \sm H\underline{\F}_2 whose generators correspond to representation spheres, while at odd primes, we see something more unusual.
hide

UBC Math

Fri 3 Nov 2017, 3:00pm
Department Colloquium
ESB 2012

A Class of Polytopes with a Remarkable Volume Formula

ESB 2012
Fri 3 Nov 2017, 3:00pm4:00pm
Abstract
We introduce a class of polytopes which we call endoskeletal. The structure of an endoskeletal polytope is determined by its internal skeleton and its volume is given by a strikingly simple formula involving a single determinant. A rudimentary knowledge of undergraduate mathematics is necessary and sufficient for understanding this talk.
hide

UC Irvine

Mon 6 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126

The Theory of Resolvent Degree  After Hamilton, Sylvester, Hilbert, Segre and Brauer

MATH 126
Mon 6 Nov 2017, 4:00pm5:00pm
Abstract
Resolvent degree is an invariant of a branched cover which quantifies how "hard" is it to specify a point in the cover given a point under it in the base. Historically, this was applied to the branched cover P^n/S_{n1} > P^n/S_n, from the moduli of degree n polynomials with a specified root to the moduli of degree n polynomials. Classical enumerative problems and congruence subgroups provide two additional sources of branched covers to which this invariant applies. In ongoing joint work with Benson Farb, we develop the theory of resolvent degree as an extension of Buhler and Reichstein's theory of essential dimension. We apply this theory to systematize an array of classical results and to relate the complexity of seemingly different problems such as finding roots of polynomials, lines on cubic surfaces, and level structures on intermediate Jacobians.
hide

Emory University

Tue 7 Nov 2017, 3:30pm
SPECIAL
Number Theory Seminar
MATH 126 (Videoconference)

Can’t you just feel the Moonshine?

MATH 126 (Videoconference)
Tue 7 Nov 2017, 3:30pm5:00pm
Abstract
(This talk is held at SFU, and is being viewed at UBC via videoconference.) Borcherds won the Fields medal in 1998 for his proof of the Monstrous Moonshine
Conjecture. Loosely speaking, the conjecture asserts that the representation theory of the Monster, the largest sporadic finite simple group, is dictated by the Fourier expansions of a distinguished set of modular functions. This conjecture arose from astonishing coincidences noticed by finite group theorists and arithmetic geometers in the 1970s. Recently, mathematical physicists have revisited moonshine, and they discovered evidence of undiscovered moonshine which some believe will have applications to string theory and 3d quantum gravity. The speaker and his collaborators have been developing the mathematical facets of this theory, and have proved the conjectures which have been formulated. These results include a proof of the Umbral Moonshine Conjecture, and Moonshine for the first sporadic finite simple group which does not occur as a subgroup or subquotient of the Monster. The most recent Moonshine (announced here) yields unexpected applications to the arithmetic elliptic curves thanks to theorems related to the Birch and SwinnertonDyer Conjecture and the Main Conjectures of Iwasawa theory for modular forms. This is joint work with John Duncan, Michael Griffin and Michael Mertens.
hide

UBC

Tue 7 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Optimal Stopping with a Probabilistic Constraint

ESB 2012
Tue 7 Nov 2017, 3:30pm4:30pm
Abstract
Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possible nonsmooth and degenerate, parabolic PDE known as an HamiltonJacobiBellman (HJB) equation. These equations are well understood using the theory of viscosity solutions, and the optimal stopping policy can be retrieved when there is some regularity and nondegeneracy of solution.
The HJB equation is commonly derived from a dynamic programming principle (DPP). After adding a probabilistic constraint, the optimal policies no longer satisfy this DPP. Instead, we can reach the HJB equation by a method related to optimal transportation, and recover a DPP for a Lagrangianrelaxation of the problem. The resulting HJB equation remains coupled through the constraint with the optimal policy (and another parabolic PDE). Solving the HJB and recovery of the optimal stopping policy is aided by considering the ``piecewisemonotonic’' structure of the stopping set.
hide

UBC

Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127

Nearequality of ribbon Schur functions

ESB 4127
Tue 7 Nov 2017, 4:00pm5:00pm
Abstract
Schur functions form the most interesting and important basis for the algebra of symmetric functions. They have connections to representation theory and algebraic geometry, and satisfy a multitude of beautiful combinatorial identities. We investigate an algebraic relationship between ribbon Schur functions, a generalization of Schur functions. More specifically, we consider when the difference between two ribbon Schur functions is a single Schur function. We will see that this nearequality phenomenon occurs for fourteen infinite families and we will present conditions under which these are the only possibilities.
hide

UBC

Wed 8 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

Anomalous diffusion

ESB 2012
Wed 8 Nov 2017, 3:00pm4:00pm
Abstract
The term ‘anomalous diffusion’ is used in the physics literature to refer to Markov processes with the property that EX_tX_0^2 grows either faster or slower than linearly. In this talk I will give a survey of results in this area, including random walks and diffusion on the Sierpinski gasket and other exact fractals, and random examples such as critical percolation clusters and the uniform spanning tree.
hide

University of California, Irvine

Wed 8 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Coincidences of homological densities, predicted by arithmetic

ESB 4133 (PIMS Lounge)
Wed 8 Nov 2017, 3:15pm4:15pm
Abstract
Basic questions in analytic number theory concern the density of one set in another (e.g. squarefree integers in all integers). Motivated by Weil's number field/function field dictionary, we introduce a topological analogue measuring the “homological density” of one space in another. In arithmetic, Euler products can be used to show that many seemingly different densities coincide in the limit. By combining methods from manifold topology and algebraic combinatorics, we discover analogous coincidences for limiting homological densities arising from spaces of 0cycles (e.g. configuration spaces of points) on smooth manifolds and complex varieties. We do not yet understand why these topological coincidences occur. This is joint work with Benson Farb and Melanie Wood.
hide

Emory University

Thu 9 Nov 2017, 3:30pm
SPECIAL
ESB 2012

PIMS  UBC Math Distinguished Colloquium: Polya’s Program for the Riemann Hypothesis and Related Problems

ESB 2012
Thu 9 Nov 2017, 3:30pm5:00pm
Details
In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's Xifunction. This hyperbolicity has only been proved for degrees d=1, 2, 3. We prove the hyperbolicity of 100% of the Jensen polynomials of every degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.
hide


Fri 10 Nov 2017, 12:00pm
Graduate Student Seminar
MATH 203

Nearequality of ribbon Schur functions

MATH 203
Fri 10 Nov 2017, 12:00pm1:00pm
Abstract
Schur functions form the most interesting and important basis for the algebra of symmetric functions. They have connections to representation theory and algebraic geometry, and satisfy a multitude of beautiful combinatorial identities. We investigate an algebraic relationship between ribbon Schur functions, a generalization of Schur functions. More specifically, we consider when the difference between two ribbon Schur functions is a single Schur function. We will see that this nearequality phenomenon occurs for fourteen infinite families and we will present conditions under which these are the only possibilities.
hide

Department of Mathematics, UBC

Tue 14 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces

ESB 4133 (PIMS Lounge)
Tue 14 Nov 2017, 12:30pm1:30pm
Abstract
Eikonal equation is a fundamental nonlinear PDE that find vast applications. One particular example is to compute geodesic distance on a curved surface through solving an eikonal equation defined on the surface (surface eikonal equations). However, there are only very few literatures on solving surface eikonal equations numerically, due to the complication from the surface geometry. In this talk, we present a simple and efficient numerical algorithm to solve surface eikonal
equations on general implicit surfaces.
hide

UBC & Univ. Basel

Tue 14 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Conformal metrics on \mathbb{R}^n with arbitrary total Qcurvature

ESB 2012
Tue 14 Nov 2017, 3:30pm4:30pm
Abstract
I will talk about the existence of solution to the Qcurvature problem
\begin{align}\label{1}
(\Delta)^\frac n2 u=Qe^{nu}\quad\text{in }\mathbb{R}^n,\quad \kappa:=\int_{\mathbb{R}^n}Qe^{nu}dx<\infty,
\end{align}
where Q is a nonnegative function and n>2. Geometrically, if u is a solution to \eqref{1} then Q is the Qcurvature of the conformal metric g_u = e^{2u}dx^2 (dx^2 is the Euclidean metric on \mathbb{R}^n), and \kappa is the total Qcurvature of g_u.
Under certain assumptions on Q around origin and at infinity, we prove the existence of solution to \eqref{1} for every \kappa > 0.
hide

University of Puget Sound

Tue 14 Nov 2017, 4:00pm
ESB 4127

Authoring Open Textbooks with PreTeXt

ESB 4127
Tue 14 Nov 2017, 4:00pm5:00pm
Details
PreTeXt is a new markup language for describing structured scholary documents, such as research articles and textbooks. It was designed originally to meet the demands of communicating mathematics, but has now been used to author books on computer science, physics, music theory, and composition (writing). It is the basis for the mobile edition of UBC's CLP calculus text. A key feature of PreTeXt is highfidelity conversions to print, PDF, online (HTML), Jupyter notebooks, and soon EPUB.
After an introduction, I will demonstrate some of the more interesting extra capabilities of the online versions, including embedded live Sage code and WeBWorK automated homework problems. Recent advances in producing Jupyter notebooks will also be demonstrated.
Project website: mathbook.pugetsound.edu
hide

UBC

Wed 15 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS Videoconference room

Coupling Mechanical Tension and GTPase Signaling to Generate Cell and Tissue Dynamics

PIMS Videoconference room
Wed 15 Nov 2017, 2:00pm2:45pm
Abstract
Regulators of the actin cytoskeleton such Rho GTPases can modulate forces developed in cells by promoting actomyosin contraction. At the same time, through mechanosensing, tension is known to affect the activity of Rho GTPases.
What happens when these effects act in concert? Using a minimal model (1 GTPase coupled to a KelvinVoigt element), we show that twoway feedback between signaling (“RhoA”) and mechanical tension (stretching) leads to a spectrum of cell behaviors, including contracted or relaxed cells, and cells that oscillate between these extremes. When such “model cells” are connected to one another in a row or in a 2D sheet (“epithelium”), we observe waves of contraction/relaxation and GTPase activity sweeping through the tissue. The minimal model lends itself to full bifurcation analysis, and suggests a mechanism that explains behavior observed in the context of development and collective cell behavior.
hide

University of Washington

Wed 15 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

The Conformal Continuum Random Tree

ESB 2012
Wed 15 Nov 2017, 3:00pm4:00pm
Abstract
I will begin with a gentle introduction to "conformal welding" from the probabilistic viewpoint, which is at the heart of Scott Sheffields "quantum zipper" as well as Malliavin's and his coauthors work on Brownian measures on the group of circle homeomorphisms. Then I will describe a conformal welding problem involving to the CRT, discuss the existence of its solution (joint work with Peter Lin), and describe how it arises as the limit of certain dessin d'enfants.
hide

Wayne State University

Wed 15 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133

Tensortriangulated number theory

ESB 4133
Wed 15 Nov 2017, 3:15pm4:15pm
Abstract
In the 1970s, work of Adams, Baird, Bousfield, and Ravenel gave a description of the orders of the KU[1/2]local stable homotopy groups of spheres as the denominators of special values of the Riemann zetafunction. Meanwhile, Lichtenbaum conjectured a formula, ultimately proven 30 years later as a consequence of the Iwasawa main theorem and the norm residue theorem, relating the orders of the algebraic Kgroups of totally real number rings to special values of their Dedekind zetafunctions. In this talk I will describe two general approaches, an analytic approach and an algebraic approach, to a general kind of number theory that arises in any tensor triangulated category: this is a general framework for the above results and gneralizations of them, and which aims to describe the orders of Bousfieldlocalized stable homotopy groups of finite spectra in terms of special values of Lfunctions. Then I'll show off some new results in this framework, in particular, a "universal" description of the KUlocal homotopy groups of the Moore spectrum S/p in terms of Lvalues, and as a consequence, a proof of a certain (infinite) family of cases of Leopoldt's conjecture, by counting orders of homotopy groups.
hide

Université de Montréal

Fri 17 Nov 2017, 11:00am
Number Theory Seminar
GEOG 101

A geometric generalization of the square sieve and applications to cyclic covers

GEOG 101
Fri 17 Nov 2017, 11:00am12:00pm
Abstract
We study a generalization of the quadratic sieve to a geometric setting. We apply this to counting points of bounded height on an lcyclic cover over the rational function field and we consider a question of Serre. In addition to the geometric quadratic sieve, we use Fourier analysis over function fields, deep results of Deligne and Katz about cancellation of mixed character sums over finite fields, and a bound on the number of points of bounded height due to Browning and Vishe.
This is joint work with A. Bucur, A. C. Cojocaru, and L. B. Pierce.
hide

UBC

Fri 17 Nov 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMSUBC Distinguished Colloquium: The role of random models in compressed sensing and matrix completion

ESB 2012
Fri 17 Nov 2017, 3:00pm4:00pm
Abstract
Random models lead to a precise and comprehensive theory of compressed sensing and matrix completion. The number of random linear measurements needed to recover a sparse signal, or a lowrank matrix, or, more generally, a structured signal, are now well understood. This is appealing in practice since it helps to determine the pros and cons of different models and gives a benchmark for success. Nevertheless, a practitioner with a fixed data set will wonder: Can they apply theory based on randomness? Is there any hope to get the same guarantees? We discuss these questions in compressed sensing and matrix completion, which, surprisingly, seem to have divergent answers.
Yaniv Plan is the 2016 winner of the PIMS UBC Math Sciences Prize.
hide

Idaho

Mon 20 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126

Equations for surfaces in projective fourspace

MATH 126
Mon 20 Nov 2017, 4:00pm5:00pm
Abstract
This talk is concerned with the question of the minimal number of equations necessary to define a given projective variety schemetheoretically. Every hypersurface is cut out by a single polynomial schemetheoretically (also settheoretically and ideal theoretically). Therefore the question is more interesting if a variety has a higher codimension. In this talk, we focus on the case when the codimension is two. If a variety in projective nspace has codimension two, then the minimal number of polynomials necessary to cut out the variety schemetheoretically is between 2 and n+1. However the varieties cut out by fewer than n+1, but more than 2 polynomials seem very rare. The main goal of this talk is to discuss conditions for a nonsingular surface in projective fourspace to be cut out by three polynomials.
hide

Institute of Applied Mathematics, UBC

Tue 21 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Likelihoodfree methods: Challenges in fitting individualbased models to epidemiological data

ESB 4133 (PIMS Lounge)
Tue 21 Nov 2017, 12:30pm1:30pm
Abstract
Complex individualbased models abound in epidemiology and ecology. Fitting these models to data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, and the complex models may take a long time to run, requiring parameter selection procedures. Approximate Bayesian Computation has been proposed as a likelihoodfree method in resolving these issues, however requires careful selection of summary statistics and annealing scheme. I compare this procedure directly to standard methodologies where the likelihood exists, Markovchain Monte Carlo and maximum likelihood. This is then applied to a complex individualbased simulation for lymphatic filariasis, a human parasitic disease, which affects over 120 million individuals internationally. Finally, I will discuss a new approach to individualbased model fitting by constructing a synthetic likelihood using mixture density networks.
hide

University of Chile

Tue 21 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Asymptotic stability for some nonlinear KleinGordon equations for odd perturbations in the energy space

ESB 2012
Tue 21 Nov 2017, 3:30pm4:30pm
Abstract
Showing asymptotic stability in one dimensional nonlinear KleinGordon equations is a notoriously difficult problem. In this talk I will describe an approach based on virial estimates which allows to prove it in case when only odd perturbations are allowed. In particular I will discuss asymptotic stability of the kink in the \phi^{^4} model.
hide

Brown University

Tue 21 Nov 2017, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATH 126

The Picard group of the moduli of smooth complete intersections of two quadrics

MATH 126
Tue 21 Nov 2017, 4:00pm5:00pm
Abstract
We study the moduli space of smooth complete intersections of two quadrics by relating it to the geometry of the singular members of the corresponding pencil. We give a new description for this parameter space by using the fact that two quadrics can be simultaneously diagonalized. Using this description we can compute the Picard group, which always happens to be cyclic. For example, we show that the Picard group of the moduli stack of smooth degree 4 Del Pezzo surfaces is Z/4Z.
This is a joint work with Giovanni Inchiostro.
hide

UPenn

Tue 21 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127

TBD

ESB 4127
Tue 21 Nov 2017, 4:00pm10:00am
Abstract
hide

UBC, Math

Wed 22 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)

Pattern formation on a Slowly Flattening Spherical Cap: A closest Point Method Approach.

PIMS (ESB 4th floor)
Wed 22 Nov 2017, 2:00pm3:00pm
Abstract
Pattern formation is quite recurrent in the natural world such as in the stripes or dots in some animals' coat. The morphogen hypothesis introduced by Turing in 1952 has been used and studied extensively to explain such patterns on several different domain shapes. In this talk we use the spherical cap domain. This is motivated by the shape of the the tip of a conifer embryo, where branching patterns emerge as the tip flattens. Previous results have been achieved to characterize the different patterns obtained on the cap for different radius and curvature values for a constant domain in time. Here we work with a nonautonomous domain with slowly decreasing curvature. We start with previously obtained results from center manifold reduction and finite elements methods. After that we continue by broadly introducing the closest point method for solving PDEs, explain how we use the method on a flattening spherical cap and end with some very preliminary results.
hide

UBC

Wed 22 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

Spin systems and some natural questions in probability

ESB 2012
Wed 22 Nov 2017, 3:00pm4:00pm
Abstract
It has long been known that many interesting questions in probability have a formulation in the language of spin systems. However, it has been only rather recently that the methods developed for spin systems were applied to finally obtain answers to some of these questions. In this talk, I will discuss three such questions, about the weakly selfavoiding walk, the vertex reinforced jump process, and random band matrices. I will then show the audience some technical lemmas that are at the heart of the analysis of spin systems.
hide

UBC

Wed 22 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

The A1 calculation of the 4th homotopy group of the 6,3sphere and a conjecture of Suslin.

ESB 4133 (PIMS Lounge)
Wed 22 Nov 2017, 3:15pm4:15pm
Abstract
The algebraic Ktheory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor Ktheory and denoted K^M. In the 1980s, Andrei Suslin constructed a map K_n(F) > K^M_n(F), and conjectured that the image was the subgroup (n1)! K^M_n(F). He also proved the conjecture for n<=3. For n=5, we reinterpret the construction as a construction in the A1 homotopy groups of spheres and BGL, and by calculating these groups, show that the conjecture is true in this case as well. This represents part of a joint project with Aravind Asok, Jean Fasel and Kirsten Wickelgren.
hide

Texas A&M

Thu 23 Nov 2017, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATX 1102

Irrational Toric Varieties

MATX 1102
Thu 23 Nov 2017, 4:00pm5:00pm
Abstract
Classical toric varieties come in two flavours: Normal toric varieties are given by rational fans in R^n. A (not necessarily normal) affine toric variety is given by finite subset A of Z^n. When A is homogeneous, it is projective. Applications of mathematics have long studied the positive real part of a toric variety as the main object, where the points A may be arbitrary points in R^n. For example, in 1963 Birch showed that such an irrational toric variety is homeomorphic to the convex hull of the set A.
Recent work showing that all Hausdorff limits of translates of irrational toric varieties are toric degenerations suggested the need for a theory of irrational toric varieties associated to arbitrary fans in R^n. These are R^n_>equivariant cell complexes dual to the fan. Among the pleasing parallels with the classical theory is that the space of Hausdorff limits of the irrational projective toric variety of a finite set A in R^n is homeomorphic to the secondary polytope of A.
hide


Fri 24 Nov 2017, 12:00pm
Graduate Student Seminar
MATH 203

Proofs in 3 Bits or Less

MATH 203
Fri 24 Nov 2017, 12:00pm1:00pm
Abstract
There are some proofs I'm never going to get around to understanding. Shinichi Mochizuki's 2012 proof of the ABC conjecture amounts to 500 pages. The best mathematicians still struggle to understand Mochizuki's techniques today. The entire classification of finite simple groups amounts to 100000200000 pages!
Mathematical logic tells us that theorems exist whose shortest proofs are arbitrarily unreadable. However, mathematicians have recently discovered that any `computationally feasible' theorem has a `random proof' which is only 3 letters long! In this talk I present the basic ideas behind these `probabilistically checkable proofs', with applications to computational complexity, cryptography, and the foundational limitations of machine learning.
The talk requires no background; only a vague sense of mathematical curiosity is required to enjoy the discussion the most important results in theoretical computing science in the past 20 years.
hide

Columbia

Mon 27 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126

Arithmetic representations of fundamental groups

MATH 126
Mon 27 Nov 2017, 4:00pm5:00pm
Abstract
Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of the Galois group of k on the fundamental group of X, and prove several fundamental structural results about this action.
As a sample application of our techniques, we show that if X is a normal variety over a field of characteristic zero, and p is a prime, then there exists an integer N=N(X,p) such that any nontrivial padic representation of the fundamental group of X, which arises from geometry, is nontrivial mod p^N.
hide

PhD Candidate: Shirin Boroushaki
Mathematics, UBC

Mon 27 Nov 2017, 4:00pm
SPECIAL
Room 200, Graduate Student Centre, UBC

PhD Oral Exam: A Selfdual Approach to Stochastic Partial Differential Equations

Room 200, Graduate Student Centre, UBC
Mon 27 Nov 2017, 4:00pm6:00pm
Details
This thesis consists of two parts. In the first, we address the issue that — unlike their deterministic counterparts — stochastic differential equations have never been formulated as stationary states of some energy functionals on spaces of stochastic processes. We show how the selfdual variational calculus can remedy the situation by providing a natural variational approach for the resolution of a number of nonlinear stochastic partial differential equations driven by monotone operators and additive or nonadditive noise. Such operators can be gradients of convex energy or in divergence form. These equations are used to model population dynamics in biology, evolution of a fluid velocity and the turbulence in physics and also in modelling of stock prices and the risky assets in finance.
In the second part of the thesis, we use methods from optimal transport to address functional inequalities on the ndimensional sphere. In particular, we prove EnergyEntropy duality formulas that yield and improve the celebrated MoserOnofri inequalities on 2dimensional sphere.
hide

Institute of Applied Mathematics, UBC

Tue 28 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Modelling Lithium Ion Batteries

ESB 4133 (PIMS Lounge)
Tue 28 Nov 2017, 12:30pm1:30pm
Abstract
I am working with colleagues on several projects modelling Lithium Ion batteries. Experimental results are fit to simple models of performance and "State of Health", a vaguely defined measure of the change of battery characteristics with use and age. This project is a collaboration with a local company, JTT electronics. Opening the hood of a battery reveals an interesting mix of multiscale and multiphase transport. Recent progress on categorizing models in the literature based on an asymptotic parameter, and computational approaches to the resulting structure, will be shown. All projects are "work in progress". Collaborators include Arman Bonakdarpour, Bhushan Gopaluni, Matt Hennessey, David Kong, Iain Moyles, and Tim Myers.
hide

UBC, Math

Wed 29 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS Videoconference room

Data processing and pattern nucleation for the MinD system.

PIMS Videoconference room
Wed 29 Nov 2017, 2:00pm3:00pm
Abstract
The Min system is an important regulator network involved in Ecoli cell division. However, although the effects and chemicals involved in this network are known, there still remain a variety of hypotheses about the exact reactions and mechanisms involved. Recent experimental work by Vecchiarelli et al. has demonstrated a large variety of reactiondiffusion induced patterns on a 2d membrane. In this talk I discuss some data processing on Vecchiarelli's data, and initial forays into the ``nucleation question'' (that is, how the particular patterns observed appear from an initially ``Homogeneous'' membrane).
hide


Wed 29 Nov 2017, 2:45pm
SPECIAL
ESB 4133 (PIMS Lounge)

PIMS Afternoon Tea

ESB 4133 (PIMS Lounge)
Wed 29 Nov 2017, 2:45pm3:15pm
Details
Update: The last PIMS Afternoon Tea of the fall semester will take place at the regular time of 2:45pm.
hide


Wed 29 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

Polluted bootstrap percolation

ESB 2012
Wed 29 Nov 2017, 3:00pm4:00pm
Abstract
Bootstrap percolation is a fundamental cellular automaton model for nucleation. Despite its simplicity, the model holds many surprises. I'll focus on how growth from sparse random seeds is affected by sparse random impurities in the medium. The answer will involve using recent oriented surface technology to construct a stegosaurus.
Based on joint work with Janko Gravner and David Sivakoff.
hide

Université ParisSaclay

Wed 29 Nov 2017, 5:00pm
Department Colloquium
As of Tuesday, Nov 28th: unfortunately this colloquium has been cancelled. ESB 2012

Update: This colloquium has been cancelled. PIMS Distinguished Colloquium: Generative Models and Optimal Transport

As of Tuesday, Nov 28th: unfortunately this colloquium has been cancelled. ESB 2012
Wed 29 Nov 2017, 5:00pm6:00pm
Abstract
A recent wave of contributions in machine learning center on the concept of generative models for extremely complex data such as natural images. These approaches provide principled ways to use deep network architectures, large datasets and automatic differentiation to come up with algorithms that are able to synthesize realistic images. We will present in this talk how optimal transport is gradually establishing itself as a valuable tool to carry out this estimation procedure.
hide

Courant Institute, NYU

Thu 30 Nov 2017, 12:00pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127 (PIMS Videoconference room)

MeanField Limits for GinzburgLandau vortices

ESB 4127 (PIMS Videoconference room)
Thu 30 Nov 2017, 12:00pm1:00pm
Abstract
GinzburgLandau type equations are models for superconductivity, superfluidity, BoseEinstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complexvalued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic GinzburgLandau equation or the GrossPitaevskii (=Schrodinger GinzburgLandau) equation.
hide

Department of Mathematics, UBC

Thu 30 Nov 2017, 12:30pm
SPECIAL
Mathematical Education
MATH 126

Using data analysis to inform multiple choices exam design

MATH 126
Thu 30 Nov 2017, 12:30pm1:30pm
Abstract
In this informal lunch talk, I will introduce several standard mathematical tools for exploring the effectiveness of multiple choice exam questions: covariance, binning, and item response theory. We will examine three tests analyzed using these methods and discuss what the results imply about how multiple choice questions should be written and how tests should be constructed. The tools above enable us to find questions that have a varying levels of discrimination between high scoring students and low scoring students, as well as rate such questions difficulty. Using this information, we will discuss what features of a question contribute to or detract from its effectiveness in measuring student performance. Finally, we will discuss the construction of the multiple choice portion of an exam and what kinds of distributions of questions serve to most effectively measure students knowledge.
hide

Université ParisSaclay

Thu 30 Nov 2017, 5:00pm
SPECIAL
ESB 2012

UBC Mathematics Lecture Series:: Regularized Optimal Transport. Part I.

ESB 2012
Thu 30 Nov 2017, 5:00pm6:30pm
Details
Optimal transport theory provides practitioners from statistics, imaging, graphics or machine learning with a very powerful toolbox to compare probability measures. These tools translate however in their original form into computational schemes that can become intractable or suffer from instability (such as nondifferentiability or estimation bias). We will present in these two lectures how a few insights from optimization theory and in particular a careful regularization can result in tools that are considerably easier to implement, run faster because they can take advantage of parallel hardware and behave better from a statistical perspective. We will highlight applications from diverse areas, from graphics and brain imaging to text analysis and parametric estimation.
hide

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