Mathematics Dept.
  Events
Jacob Denson
Fri 24 Nov 2017, 12:00pm
Graduate Student Seminar
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

Latecomers will not be admitted.
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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)
Nov. 29th PIMS Afternoon Tea has been moved to 4:30pm-5:00pm
ESB 4133 (PIMS Lounge)
Wed 29 Nov 2017, 2:45pm-3:15pm

Details

The last PIMS Afternoon Tea of the fall semester will take place before Marco Cuturi's 5:00 pm PIMS Distinguished Colloquium.
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Université Paris-Saclay
Wed 29 Nov 2017, 5:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS Distinguished Colloquium: Generative Models and Optimal Transport
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

The last PIMS Afternoon Tea/Reception of the fall semester will take place from 4:30pm - 5:00pm in the PIMS Lounge.


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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Nate Bade
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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