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 Events
Thomas Hughes
UBC
Fri 1 Apr 2016, 1:00pm
Graduate Student Seminar
Math 225
Entropy, in Information Theory and Elsewhere
Math 225
Fri 1 Apr 2016, 1:00pm-2:00am

Abstract

I will discuss the notion of entropy as it arises in information and coding theory and its central role in Shannon's classical source coding theorem. I will then, to the extent I can coherently manage, show how it generalizes to a more general notion of entropy as it arises in dynamical systems theory.

Note for Attendees

 Pizza and pop will be provided.
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Robert Kohn
Courant Institute, NYU
Fri 1 Apr 2016, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--A Variational Perspective on Wrinkling Patterns in Thin Elastic Sheets
ESB2012
Fri 1 Apr 2016, 3:00pm-4:00pm

Abstract

 Abstract: Thin sheets exhibit a daunting array of patterns. A key difficulty in their analysis is that while we have many examples, we have no  classification of the possible "patterns." I have explored an alternative viewpoint in a series of recent projects with Peter Bella, Hoai-Minh Nguyen, and others. Our goal is to identify the *scaling law* of the minimum elastic energy (with respect to the sheet thickness, and the other parameters of the problem). Success requires proving upper bounds and lower bounds that scale the same way. The upper bounds are usually easier, since nature gives us a hint. The lower bounds are more subtle, since they must be ansatz-independent. In many cases, the arguments used to prove the lower bounds help explain "why" we see particular patterns. My talk will give an overview of this activity, and details of some  examples. 
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UBC
Mon 4 Apr 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
Prime Decomposition for the index of a Brauer class
MATH 126
Mon 4 Apr 2016, 3:00pm-4:00pm

Abstract

An Azumaya algebra of degree n is an algebra locally isomorphic to an nxn matrix algebra, a concept that generalizes that of central simple algebras over fields. The Brauer group consists of equivalence classes of Azumaya algebras and the index of a class in the Brauer group is defined to be the greatest common divisor of the degrees of all Azumaya algebras in that class. 
 
Suppose p and q are relatively prime positive integers. Whereas an Azumaya algebra of degree pq need not, in general, decompose as a tensor product of algebras of degrees p and q, we show that a Brauer class of index pq does decompose as a sum of Brauer classes of indices p and q. The argument requires only the representation theory of GLn, and therefore establishes the result in contexts where one does not have recourse to the theory of fields, for instance in the theory of Azumaya algebras on topological spaces.
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PhD Candidate: Pooya Ronagh
Mathematics, UBC
Tue 5 Apr 2016, 11:00am SPECIAL
Room 200, Graduate Student Centre, 6371 Crescent Rd., UBC
Doctoral Exam: The Inertia Operator and Hall Algebra of Algebraic Stacks
Room 200, Graduate Student Centre, 6371 Crescent Rd., UBC
Tue 5 Apr 2016, 11:00am-1:00pm

Details

ABSTRACT: This work leads to a simple and geometric framework for defining generalized Donaldson-Thomas invariants. We view the inertia construction of algebraic stacks as an operator on the Grothendieck groups of various categories of algebraic stacks. We expect to show that this operator is diagonalizable and the Donaldson-Thomas theory of various moduli spaces can be defined in term of the eigenprojections of this operator.

We are interested in showing that the inertia operator is (locally finite and) diagonalizable over for instance the field of rational functions of the motivic class of the affine line. This is proved for the Grothendieck group of Deligne-Mumford stacks and the category of quasi-split Artin stacks.

Motivated by the quasi-splitness condition we then develop a theory of linear algebraic stacks and algebroids, and define a space of stack functions over a linear algebraic stack. We prove diagonalization of the semisimple inertia for the space of stack functions. A different family of operators is then defined that are closely related to the semisimple inertia. These operators are diagonalizable on the Grothendieck ring itself (i.e. without inverting elements) and provide ways of computing eigenprojections of elements with respect to the semisimple inertia.

We then define a graded structure on the Hall algebra on the space of stack functions in terms of the eigenspaces of the semisimple inertia. The commutative and non-commutative products of the Hall algebra respect the graded structure of the Hall algebra and they coincide on the associated graded algebra. This result provides a geometric way of defining a Lie subalgebra of virtually indecomposables. An $\epsilon$-element associated to an algebroid is defined and shown to be in the space of virtually indecomposables.
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PhD Student, Computer Science Department, UBC
Tue 5 Apr 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Is Greedy Coordinate Descent a Terrible Algorithm?
ESB 4133 (PIMS Lounge)
Tue 5 Apr 2016, 12:30pm-2:00pm

Abstract

There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov, who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result suggests that we should never use the Gauss-Southwell rule, as it is typically much more expensive than random selection. However, the empirical behaviours of these algorithms contradict this theoretical result: in applications where the computational costs of the selection rules are comparable, the Gauss-Southwell selection rule tends to perform substantially better than random coordinate selection. We give a simple analysis of the Gauss-Southwell rule showing that---except in extreme
cases---it's convergence rate is faster than choosing random coordinates. Further, we (i) show that exact coordinate optimization improves the convergence rate for certain sparse problems, (ii) propose a Gauss-Southwell-Lipschitz rule that gives an even faster convergence rate given knowledge of the Lipschitz constants of the partial derivatives, and (iii) analyze proximal-gradient variants of the Gauss-Southwell rule.

Joint work with Mark Schmidt, Issam Laradji, Michael Friedlander and Hoyt Koepke.

Note for Attendees

Sushi lunch will be served at 12:20 p.m.
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University of Calgary
Tue 5 Apr 2016, 4:00pm
Number Theory Seminar
room MATH 126 (note different day and time)
On the combinatorial structure of Arthur packets: p-adic symplectic and orthogonal groups
room MATH 126 (note different day and time)
Tue 5 Apr 2016, 4:00pm-5:00pm

Abstract

The irreducible smooth representations of Arthur class are the local components of automorphic representations. They are conjectured to be parametrized by the Arthur parameters, which form a subset of the usual Langlands parameters. The set of irreducible representations associated with a single Arthur parameter is called an Arthur packet. Following Arthur's classification theory of automorphic representations of symplectic and orthogonal groups, the Arthur packets are now known in these cases. On the other hand, Moeglin independently constructed these packets in the p-adic case by using very different methods. In this talk, I would like to describe a combinatorial procedure to study the structure of the Arthur packets following the works of Moeglin. As an application, we show the size of Arthur packets in these cases can be given by counting integral (or half-integral) points in certain polytopes.
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Wed 6 Apr 2016, 10:00am
Math Education Research Reading
Math 126
"Facilitating Instructor Adoption of Inquiry-Based Learning in College Mathematics"
Math 126
Wed 6 Apr 2016, 10:00am-11:00am

Abstract

 
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UBC Math
Wed 6 Apr 2016, 3:00pm
Probability Seminar
ESB 2012
The boundary of the support of super-Brownian Motion
ESB 2012
Wed 6 Apr 2016, 3:00pm-4:00pm

Abstract

We will study the edge of the support of 1-dimensional super-brownian motion.  The local behaviour of the density, Hausdorff dimension of the boundary, and rates of convergence of certain solutions to singular semilinear heat equations studied in the pde literature are all expressed in terms of a particular eigenvalue of a killed Ornstein-Uhlenbeck operator.  Time permitting, we will discuss some possible connections with pathwise uniqueness questions for some related stochastic pde's. This is joint work with Carl Mueller and Leonid Mytnik.
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Oklahoma State University
Thu 7 Apr 2016, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
The two-dimensional Boussinesq equations with partial dissipation
ESB 4127
Thu 7 Apr 2016, 3:30pm-4:30pm

Abstract

The Boussinesq equations concerned here model geophysical flows such
as atmospheric fronts and ocean circulations. In addition, they play an
important role in the study of Rayleigh-Benard convection. Mathematically
the 2D Boussinesq equations serve as a lower-dimensional model of the 3D
hydrodynamics equations. In fact, the 2D Boussinesq equations retain some
key features of the 3D Euler and the Navier-Stokes equations such as the
vortex stretching mechanism. The global regularity problem on the 2D
Boussinesq equations with partial or fractional dissipation has attracted
considerable attention in the last few years. This talk presents recent
developments in this direction. In particular, we detail the global regularity
result on the 2D Boussinesq equations with vertical dissipation as
well as some recent work for the 2D Boussinesq equations with general
critical dissipation.
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PdD Candidate: Junho Hwang
Mathematics, UBC
Mon 11 Apr 2016, 12:30pm SPECIAL
Room 225, Mathematics Building, UBC
Doctoral Exam: On the Stability and Moduli of Noncommutative Algebras
Room 225, Mathematics Building, UBC
Mon 11 Apr 2016, 12:30pm-2:30pm

Details

ABSTRACT: We study stability of 3-dimensional quadratic AS-regular algebras and their moduli.

A quadratic algebra defined by a triple (E, L, σ) is stable if there is no node or line component of E fixed by σ. We first prove stability of the twisted homogeneous coordinate ring B(E, L, σ) by Riemann-Roch and exploiting noncommutativity. Then we lift stability to that of the quadratic algebra A(E, L, σ), by analyzing the central element c3 where B=A/(c3).

We study a coarse moduli space for each type, A, B, E, H, S. S-equivalence of strictly semistable algebras is studied. We compute automorphisms of AS-regular algebras and of those that appear in the boundary of the moduli. We found complete DM-stacks for 2,3-truncated algebras.

Type B algebra as Zhang twist of type A is studied. Exceptional algebras appear in the exceptional divisor of a blowing-up at a degenerate algebra in the moduli of 3-truncations. 2-unstable algebras are studied.
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Karlsruhe Institute of Technology (KIT)
Tue 12 Apr 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012
Limits of alpha-harmonic maps
ESB2012
Tue 12 Apr 2016, 3:30pm-4:30pm

Abstract

 I will discuss a recent joint work with A. Malchiodi (Pisa) and M. Micallef (Warwick) in which we show that not every harmonic map can be approximated by a sequence of alpha-harmonic maps.
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Julien Courtiel
Tue 12 Apr 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Terminal chords in connected diagrams chords
ESB 4127
Tue 12 Apr 2016, 4:00pm-5:00pm

Abstract

 Maybe often underestimated, chord diagrams and their
enumeration appear in numerous mathematical areas: quantum field theory,
knot theory,  graph sampling, data structure analysis, and
bioinformatics. The results presented in this talk, fruits of a
collaboration with Karen Yeats, are part of the quantum field theory
framework. In fact, the solutions to certain Dyson-Schwinger equations
can be defined in terms of connected chord diagrams with a particular
parameter: the terminal chords.
 
We study some statistics about these terminal chords: their asymptotic
number, the position of the first terminal chord, etc. We establish the
means, the variances and the limit laws of all these variables, and show
the physics applications. We also explain why the classical techniques
of combinatorics do not directly work, and we give some insights on how
to get around this problem.
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University of British Columbia
Wed 13 Apr 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Minimal volume cusped hyperbolic 3-manifolds and their groups.
ESB 4133 (PIMS Lounge)
Wed 13 Apr 2016, 3:15pm-4:15pm

Abstract

For any non-negative integer n there exist n-cusped hyperbolic 3-manifolds of minimal possible volume.  They are sometimes not unique.  For example there are exactly two distinct minimal 1-cusped examples: the figure eight complement, and another which is not a knot complement.  Similarly there are distinct 2-cusped examples.  I will show how these examples differ in terms of properties of their fundamental groups.  In particular, in the pairs of examples in the 1 or 2 cusped case, one has bi-orderable fundamental group while the other’s group is not orderable.  This is a preliminary announcement of work in progress with Eiko Kin (Osaka).
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PhD Candidate: Tatchai Titichetrakun
Mathematics, UBC
Thu 14 Apr 2016, 12:30pm SPECIAL
Room 200, Graduate Student Centre, 6371 Crescent Rd., UBC
Doctoral Exam: A Multidimensional Szemeredi's Theorem in the Primes
Room 200, Graduate Student Centre, 6371 Crescent Rd., UBC
Thu 14 Apr 2016, 12:30pm-2:30pm

Details

ABSTRACT: In this thesis, we study methods in the proof of Green-Tao’s theorem on existence of arithmetic progressions in dense subsets of primes (or almost primes) and prove some of its generalizations. Firstly, we study the Goldston-Yildirim sieve on almost primes which is used to prove pseudorandom conditions for almost primes in the work of Green and Tao. We combine the Goldston-Yildirim sieve with circle method of Birch to obtain a lower bound on the number of almost prime solutions to high rank Diophantine systems. Secondly, we apply the transference principle used in the original proof of Green-Tao’s result (simplified by Gowers using Hahn-Banach’s Theorem) to obtain a lower bound on the number of affine copies of a corner configurations in dense subsets of prime lattices in higher dimensions. The main difficulty is to deal with unbounded dual functions. Finally, we prove a hypergraph regularity lemma and removal lemma on weighted hypergraphs and obtain a lower bound on the number affine copies of any configuration in prime lattices. The key technique is the energy increment on parametric family of weighted probability spaces.
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Karl Sigmund, Professor of Mathematics
University of Vienna (1974-2013)
Thu 14 Apr 2016, 4:00pm SPECIAL
Peter Wall Institute, Seminar Room 307
PWIAS International Distinguished Fellow Public Talk: The Prisoner's Dilemma: Partners and Rivals
Peter Wall Institute, Seminar Room 307
Thu 14 Apr 2016, 4:00pm-5:00pm

Details


Abstract:
The Prisoner’s Dilemma game, the working horse for studying social traps, has recently undergone a remarkable rejuvenation. New results allow to characterize partner strategies, competitive strategies, and ZD strategies. If a player uses a partner strategy, both players can fairly share the social optimum; but a co-player preferring an unfair solution will be penalized by obtaining a reduced payoff. A player using a competitive strategy never obtains less than the co-player. A player using a ZD strategy unilaterally enforces a linear relation between the two players payoffs. These properties hold for all possible strategies of the co-player and thus cover a vast range of behaviors. The new results will be embedded in an overview covering a wide field of well-established theoretical and experimental results.

Speaker:
Karl Sigmund was Professor of Mathematics at the University of Vienna from 1974-2013, and is one of the pioneers of evolutionary game theory. He also worked on ergodic theory and dynamical systems, and biomathematics. More recently, he has increasingly turned to the history of science - with books, exhibitions, and films on the Vienna Circle.

Note for Attendees

Please register for this free event at http://events.pwias.ubc.ca/special-events

The Peter Wall Institute for Advanced Studies is located at 6331 Crescent Road, UBC campus, Vancouver.

This Public Talk is presented in collaboration with the UBC Department of Mathematics.

Reception to follow.

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Karl Sigmund, Peter Wall International Distinguished Fellow
Mathematics Professor at the University of Vienna (1974-2013)
Thu 21 Apr 2016, 4:00pm SPECIAL
Earth Sciences Bldg. (ESB) 2012, 2207 Main Mall, UBC
Gödel Einstein Mach
Earth Sciences Bldg. (ESB) 2012, 2207 Main Mall, UBC
Thu 21 Apr 2016, 4:00pm-5:00pm

Details

Abstract: Albert Einstein is usually associated with Zürich, Bern, Berlin or Princeton rather than Vienna. However, his Viennese contacts were many-sided and highly relevant for his work. Ernst Mach had a major influence on the general theory of relativity (the “Mach principle”), and Kurt Gödel discovered its most paradoxical consequence (the possibility of time travels into the past). In addition, Friedrich Adler, Hans Thirring, Erwin Schrödinger and the thinkers of the Vienna Circle were important companions of Einstein. In this lecture, Dr. Sigmund will not only trace a highly dramatic story replete with murder and flight, fakes and nervous breakdowns, but also highlight a central topic of general relativity: the interplay of gravitation and inertia, and their effects on rotating bodies.

Note for Attendees

Reception before the lecture will be held in ESB 4133 from 3:30--4:00 p.m.
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