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University of Alberta at Edmonton
Wed 1 Nov 2017, 3:00pm
Probability Seminar
ESB 2012
Feynman-Kac formula for the stochastic heat equation driven by general Gaussian noises
ESB 2012
Wed 1 Nov 2017, 3:00pm-4:00pm

#### Abstract

In this talk  I will  present some results on stochastic heat equations driven by a Gaussian noises. I will focus on Feynman-Kac 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 so-called intermittency. The Driving Gaussian noises include fractional Brownian fields of Hurst parameters greater or smaller than 1/2.
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Krishanu Sankar
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, 3:15pm-4:15pm

#### Abstract

In episode 2 of the series, I will turn my attention to the setting of G-equivariant stable homotopy theory, where G is an abelian p-group. 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.

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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, 3:00pm-4:00pm

#### 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.

#### Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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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, 4:00pm-5:00pm

#### 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_{n-1} -> 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.

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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, 3:30pm-5:00pm

#### 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 Swinnerton-Dyer Conjecture and the Main Conjectures of Iwasawa theory for modular forms. This is joint work with John Duncan, Michael Griffin and Michael Mertens.
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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, 3:30pm-4:30pm

#### Abstract

Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possible non-smooth and degenerate, parabolic PDE known as an Hamilton-Jacobi-Bellman (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 non-degeneracy 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 Lagrangian-relaxation 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 piecewise-monotonic’' structure of the stopping set.
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Foster Tom
UBC
Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127
Near-equality of ribbon Schur functions
ESB 4127
Tue 7 Nov 2017, 4:00pm-5:00pm

#### 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 near-equality phenomenon occurs for fourteen infinite families and we will present conditions under which these are the only possibilities.
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UBC
Wed 8 Nov 2017, 3:00pm
Probability Seminar
ESB 2012
Anomalous diffusion
ESB 2012
Wed 8 Nov 2017, 3:00pm-4:00pm

#### Abstract

The term ‘anomalous diffusion’ is used in the physics literature to refer to Markov processes with the property that E|X_t-X_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.
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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, 3:15pm-4:15pm

#### Abstract

Basic questions in analytic number theory concern the density of one set in another (e.g. square-free 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 0-cycles (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.

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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, 3:30pm-5:00pm

#### Details

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's Xi-function. 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.

#### Note for Attendees

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Foster Tom
Fri 10 Nov 2017, 12:00pm
MATH 203
Near-equality of ribbon Schur functions
MATH 203
Fri 10 Nov 2017, 12:00pm-1:00pm

#### 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 near-equality phenomenon occurs for fourteen infinite families and we will present conditions under which these are the only possibilities.
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Tony Wong
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, 12:30pm-1:30pm

#### 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.

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Ali Hyder
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 Q-curvature
ESB 2012
Tue 14 Nov 2017, 3:30pm-4:30pm

#### Abstract

I will talk about the existence of solution to the Q-curvature problem

\begin{align}\label{1}
\end{align}

where Q is a non-negative function and n>2. Geometrically, if u is a solution to \eqref{1} then Q is the Q-curvature 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 Q-curvature 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.

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University of Puget Sound
Tue 14 Nov 2017, 4:00pm
ESB 4127
Authoring Open Textbooks with PreTeXt
ESB 4127
Tue 14 Nov 2017, 4:00pm-5:00pm

#### 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 high-fidelity 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

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Cole Zmurchok
UBC
Wed 15 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS Video-conference room
Coupling Mechanical Tension and GTPase Signaling to Generate Cell and Tissue Dynamics
PIMS Video-conference room
Wed 15 Nov 2017, 2:00pm-2:45pm

#### 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 Kelvin-Voigt element), we show that two-way 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.
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University of Washington
Wed 15 Nov 2017, 3:00pm
Probability Seminar
ESB 2012
The Conformal Continuum Random Tree
ESB 2012
Wed 15 Nov 2017, 3:00pm-4:00pm

#### 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.
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Wayne State University
Wed 15 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133
Tensor-triangulated number theory
ESB 4133
Wed 15 Nov 2017, 3:15pm-4:15pm

#### 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 zeta-function. 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 K-groups of totally real number rings to special values of their Dedekind zeta-functions. 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 Bousfield-localized stable homotopy groups of finite spectra in terms of special values of L-functions. Then I'll show off some new results in this framework, in particular, a "universal" description of the KU-local homotopy groups of the Moore spectrum S/p in terms of L-values, and as a consequence, a proof of a certain (infinite) family of cases of Leopoldt's conjecture, by counting orders of homotopy groups.

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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, 11:00am-12:00pm

#### Abstract

We study a generalization of the quadratic sieve to a geometric setting. We apply this to counting points of bounded height on an l-cyclic 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.
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Yaniv Plan
UBC
Fri 17 Nov 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium: The role of random models in compressed sensing and matrix completion
ESB 2012
Fri 17 Nov 2017, 3:00pm-4:00pm

#### 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 low-rank 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.

#### Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Idaho
Mon 20 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126
Equations for surfaces in projective four-space
MATH 126
Mon 20 Nov 2017, 4:00pm-5:00pm

#### Abstract

This talk is concerned with the question of the minimal number of equations necessary to define a given projective variety scheme-theoretically. Every hypersurface is cut out by a single polynomial scheme-theoretically (also set-theoretically 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 n-space has codimension two, then the minimal number of polynomials necessary to cut out the variety scheme-theoretically 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 non-singular surface in projective four-space to be cut out by three polynomials.
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Mike Irvine
Institute of Applied Mathematics, UBC
Tue 21 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Likelihood-free methods: Challenges in fitting individual-based models to epidemiological data
ESB 4133 (PIMS Lounge)
Tue 21 Nov 2017, 12:30pm-1:30pm

#### Abstract

Complex individual-based 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 likelihood-free 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, Markov-chain Monte Carlo and maximum likelihood. This is then applied to a complex individual-based simulation for lymphatic filariasis, a human parasitic disease, which affects over 120 million individuals internationally. Finally, I will discuss a new approach to individual-based model fitting by constructing a synthetic likelihood using mixture density networks.
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Michal Kowalczyk
University of Chile
Tue 21 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Asymptotic stability for some nonlinear Klein-Gordon equations for odd perturbations in the energy space
ESB 2012
Tue 21 Nov 2017, 3:30pm-4:30pm

#### Abstract

Showing asymptotic stability in one dimensional nonlinear Klein-Gordon 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.
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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, 4:00pm-5:00pm

#### 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.

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UPenn
Tue 21 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127
TBD
ESB 4127
Tue 21 Nov 2017, 4:00pm-10:00am

#### Abstract

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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, 2:00pm-3:00pm

#### 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 non-autonomous 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.
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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, 3:00pm-4:00pm

#### 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 self-avoiding 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.
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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 6,3-sphere and a conjecture of Suslin.
ESB 4133 (PIMS Lounge)
Wed 22 Nov 2017, 3:15pm-4:15pm

#### Abstract

The algebraic K-theory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor K-theory 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 (n-1)! 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.
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Texas A&M
Thu 23 Nov 2017, 4:00pm SPECIAL
Algebraic Geometry Seminar
MATX 1102
Irrational Toric Varieties
MATX 1102
Thu 23 Nov 2017, 4:00pm-5:00pm

#### 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.

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Jacob Denson
Fri 24 Nov 2017, 12:00pm
MATH 203
Proofs in 3 Bits or Less
MATH 203
Fri 24 Nov 2017, 12:00pm-1:00pm

#### 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 100000-200000 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.
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Columbia
Mon 27 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126
Arithmetic representations of fundamental groups
MATH 126
Mon 27 Nov 2017, 4:00pm-5:00pm

#### 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 non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod p^N.

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PhD Candidate: Shirin Boroushaki
Mathematics, UBC
Mon 27 Nov 2017, 4:00pm SPECIAL
Room 200, Graduate Student Centre, UBC
PhD Oral Exam: A Self-dual Approach to Stochastic Partial Differential Equations
Room 200, Graduate Student Centre, UBC
Mon 27 Nov 2017, 4:00pm-6:00pm

#### 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 self-dual variational calculus can remedy the situation by providing a natural variational approach for the resolution of a number of non-linear stochastic partial differential equations driven by monotone operators and additive or non-additive 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 n-dimensional sphere. In particular, we prove Energy-Entropy duality formulas that yield and improve the celebrated Moser-Onofri inequalities on 2-dimensional sphere.

#### Note for Attendees

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Brian Wetton
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, 12:30pm-1:30pm

#### 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 multi-scale and multi-phase 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.  
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Alastair Jamieson-Lane
UBC, Math
Wed 29 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS Video-conference room
Data processing and pattern nucleation for the MinD system.
PIMS Video-conference room
Wed 29 Nov 2017, 2:00pm-3:00pm

#### Abstract

The Min system is an important regulator network involved in E-coli 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 reaction-diffusion 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).
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Wed 29 Nov 2017, 2:45pm SPECIAL
ESB 4133 (PIMS Lounge)
PIMS Afternoon Tea
ESB 4133 (PIMS Lounge)
Wed 29 Nov 2017, 2:45pm-3:15pm

#### Details

Update: The last PIMS Afternoon Tea of the fall semester will take place at the regular time of 2:45pm.
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Wed 29 Nov 2017, 3:00pm
Probability Seminar
ESB 2012
Polluted bootstrap percolation
ESB 2012
Wed 29 Nov 2017, 3:00pm-4:00pm

#### 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.

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Université Paris-Saclay
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, 5:00pm-6:00pm

#### 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.

#### Note for Attendees

This Colloquium is a series of talks at UBC by Marco Cuturi. He will be giving two other lectures on Thursday, Nov 30 and Friday Dec 1, 2017.
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Sylvia Serfaty
Courant Institute, NYU
Thu 30 Nov 2017, 12:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127 (PIMS Videoconference room)
Mean-Field Limits for Ginzburg-Landau vortices
ESB 4127 (PIMS Videoconference room)
Thu 30 Nov 2017, 12:00pm-1:00pm

#### Abstract

Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued 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 Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.
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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, 12:30pm-1:30pm

#### 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.
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Université Paris-Saclay
Thu 30 Nov 2017, 5:00pm SPECIAL
ESB 2012
UBC Mathematics Lecture Series:: Regularized Optimal Transport. Part I.
ESB 2012
Thu 30 Nov 2017, 5:00pm-6:30pm

#### 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 non-differentiability 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.

#### Note for Attendees

This is the first of a two part lecture. The second part will be given on Dec, 1 2017, in ESB 2012 at the same time. Details for Part II are available here
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