Mathematics Dept.
  Events
Mathematics Department, Dalhousie
Mon 2 Nov 2015, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Swarms: from molecular dynamics to biological aggregations
ESB 2012
Mon 2 Nov 2015, 3:00pm-4:00pm

Abstract

 Aggregation is an ubiquitous natural phenomenon that pervades both the animal world and many inanimate physical systems. In the animal kingdom, group formation is observed across all levels from bacterial colonies and insect swarms to complex predator-prey interactions in fish, birds and mammals. Aggregation is also present in physical systems at all scales from the smallest (Bose-Einstein Condensates, DNA buckyball molecules, fluid vortices) to the largest (galaxies). The emergence of group behaviour is often a consequence of individuals (or atoms) following very simple rules, without any external coordination.
    In this talk I will describe some simple models of swarms that are motivated by well-known physical systems. While they may not capture the fine details of biological interactions, these models are simple enough that many of their properties can be studied analytically in great detail. This in turn can shed light about the role of swarming in biological systems. For example, is swarming behaviour helpful in avoiding a predator? Conversely, the study of biological models can also lead to new insights into related physical models.

Note for Attendees

 This is the IAM distinguished alumni lecture for 15-16. Tea served beforehand in ESB 4133 (the PIMS lounge).
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National Polytechnic School of Quito, Ecuador
Tue 3 Nov 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Multigrid second-order accurate solution of parabolic control-constrained problems
ESB 4133 (PIMS Lounge)
Tue 3 Nov 2015, 12:30pm-1:30pm

Abstract


A mesh-independent and second-order accurate multigrid strategy to solve constrained parabolic optimal control problems is presented. The resulting algorithms appear to be robust with respect to change of values of the control parameters and have the ability to accommodate constraints on the control also in the limit case of bang-bang control. Central to the development of these multigrid schemes is the design of iterative smoothers which can be formulated as local semi smooth Newton methods.

Note for Attendees

Sushi lunch will be provided.
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Jose Samper
University of Washington
Tue 3 Nov 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Relaxing the matroid axioms
ESB 4127
Tue 3 Nov 2015, 4:00pm-5:00pm

Abstract

Motivated by a question of Duval and Reiner about eigenvalues of combinatorial Laplacians, we develop a generalization of (ordered) matroid theory to wider classes of simplicial complexes. In addition to all independence complexes of matroids, each such class contains all pure shifted simplicial complexes, and it retains a little piece of matroidal spirit/structure. To achieve this, we relax the various cryptomorphic definitions of a matroid. In contrast to the matroid setting, these relaxations are independent of each other, i.e., they produce different extensions. Imposing various combinations of these new axioms allows us to provide analogues of many classical matroid structures and properties. Examples of such properties include the Tutte polynomial, lexicographic shellability of the complex, the existence of a meaningful nbc-complex and its shellability, the Billera-Jia-Reiner quasisymmetric function, and many others. We then discuss the h-vectors of complexes that satisfy our relaxed version of the exchange axiom, extend Stanley's pure O-sequence conjecture about the h-vector of a matroid, solve this conjecture for the special case of shifted complexes, and speculate a bit about the general case. Based on joint works with Jeremy Martin, Ernest Chong and Steven Klee.

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University of Washington
Wed 4 Nov 2015, 3:00pm
Probability Seminar
ESB 2012
Finitely dependent graph homomorphisms
ESB 2012
Wed 4 Nov 2015, 3:00pm-4:00pm

Abstract

When a child randomly paints a coloring book, adjacent regions receive distinct colors whereas distant regions remain independent. It took mathematicians until 2014 to replicate this effect, when Holroyd and Liggett discovered the first stationary k-dependent q-colorings. In this talk, I will discuss an extension of Holroyd and Liggett's construction which associates a canonical insertion procedure to every finite graph. The known colorings turn out to be diamonds in the rough: apart from multipartite analogues, they are the only k-dependent processes which arise from finite graphs in this manner. Time permitting, I will present extensions of these results to weighted graphs and shifts of finite type. Joint work with Alexander Holroyd.
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Eiko Kin
Osaka University
Wed 4 Nov 2015, 3:15pm
Topology and related seminars
ESB 4133
Braids, automorphisms and orderings
ESB 4133
Wed 4 Nov 2015, 3:15pm-4:15pm

Abstract

Braids represent mapping classes of the punctured disk, and hence braids induce automorphisms of the fundamental group of the punctured disk, i.e, automorphisms of the free groups. It is known that the free groups are bi-orderable. We consider which braid preserves some bi-ordering of the free group. Once we know a given braid preserves some biordering of the free group, the fundamental group of the mapping torus by the braid monodromy is bi-orderable. By using a criterion by Perron-Rolfsen together with a technique on the disk twists, we give new examples of links in the 3-sphere whose fundamental groups of the link exteriors are bi-orderable, for example, the Whitehead link, the minimally twisted 4- and 5- chain links. We also give an infinite sequence of pseudo-Anosov braids which do not preserve any bi-orderings of the free groups. As a corollary, it follows that the fundamental group of the Whitehead sister link (i.e, (-2,3,8)-pretzel link) exterior is not bi-orderable.
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Thu 5 Nov 2015, 10:30am
Math Education Research Reading
Math 126
"What students value in effective mathematics learning: a Third Wave project research study"
Math 126
Thu 5 Nov 2015, 10:30am-11:30am

Abstract

 
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UBC
Thu 5 Nov 2015, 3:30pm
Number Theory Seminar
room MATH 126
Class number formulas, volumes, and counting elliptic curves
room MATH 126
Thu 5 Nov 2015, 3:30pm-4:30pm

Abstract

This will be largely a survey of classical results: I will recall the analytic class number formula, and the Minkowski–Siegel mass formula for the "number" of quadratic forms in a genus, as well as Tamagawa's reformulation of these results as a volume computation. Then I will discuss a similar formula for the number of elliptic curves in an isogeny class, and we will see that it can again appear in two versions: one is due to Gekeler (2003) and comes from probabilistic and equidistribution considerations, and the other is due to Langlands and Kottwitz and is based on a volume computation. This talk is motivated by the joint project with Jeff Achter, Ali Altug and Luis Garcia, where we explore the connection between these two formulas and generalize Gekeler's result to counting principally polarized Abelian varieties. The talk will be completely non-technical and is not aimed at the experts (who would find most of it very familiar).
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University of Colorado, Boulder
Mon 9 Nov 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Olsson fans and logarithmic Gromov-Witten theory
MATH 126
Mon 9 Nov 2015, 3:00pm-4:00pm

Abstract

Given a scheme X and a normal crossings divisor D in X, the Olsson fan of X and D is an algebraic stack that encodes the combinatorics of the components of D and their intersections.  I will describe Olsson fans and show how they are constructed.  Then I will discuss the moduli space of stable maps from curves into an Olsson fan, and highlighting a number of applications to Gromov-Witten theory.

 

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Rob Fraser
Mathematics, UBC
Mon 9 Nov 2015, 3:00pm
Harmonic Analysis Seminar
MATX 1102
An Explicit p-adic Salem Set
MATX 1102
Mon 9 Nov 2015, 3:00pm-4:30pm

Abstract

A set that has Fourier dimension equal to its Hausdorff dimension is called a Salem set. Kaufman showed in 1981 that the well-approximable numbers of order \tau are a Salem set with dimension \frac{2}{\tau + 1}. In this joint work with Kyle Hambrook, we attempt to show that the well-approximable numbers in the p-adics of order \tau form a Salem set of dimension \frac{2}{\tau}.
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Tier 1 Canada Research Chair in the Department of Computer Science, UBC
Tue 10 Nov 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Biomechanical Modeling and Simulation of Human Movement
ESB 4133 (PIMS Lounge)
Tue 10 Nov 2015, 12:30pm-2:00pm

Abstract


Our goal is to develop large scale computational models of the human biomechanical system. Such models have a wide range of applications, ranging from computer graphics to human health.  Despite the long history of research in this area, current models have significant shortcomings. I will first outline some of these problems and their solutions, including the proper accounting of muscle mass and the role of the giant protein titin in the molecular mechanisms of force production in muscles.

In the second part of the talk I will discuss numerical methods for simulating large scale musculoskeletal systems. Biological soft tissues are usually simulated using a Lagrangian discretization, following the standard practice in solid mechanics. However, realistic systems have many muscles and tendons that are highly constrained by each other and by connective tissues. Dealing with these constraints pose significant challenges for the traditional approach. Instead, I will advocate the use of Eulerian (and Eulerian-on-Lagrangian) discretizations. I will demonstrate recent results using this approach in simulating the tendon networks of the hand, human skin, and multiple muscles in contact.

Note for Attendees

Sushi lunch will be provided.
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UCLA
Tue 10 Nov 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Hook-length formulas for skew shapes
ESB 4127
Tue 10 Nov 2015, 4:00pm-5:00pm

Abstract

The celebrated hook-length formula of Frame, Robinson and Thrall from 1954 gives a product formula for the number of standard Young tableaux of straight shape. No such product formula exists for the number of standard Young tableaux of skew shapes. In 2014, Naruse announced a formula for skew shapes as a positive sum of products of hook-lengths proved using equivariant cohomology and excited diagrams of Ikeda-Naruse and Kreiman. We prove Naruse's formula combinatorially and we give two q-analogues of this formula involving semistandard Young tableaux and reverse plane partitions of skew shape. The first q-analogue is proved algebraically. We show that the restricted Hillman-Grassl correspondence is a bijection explaining these q-analogues. Joint work with Igor Pak and Greta Panova.

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Tata Institute of Fundamental Research
Thu 12 Nov 2015, 3:30pm
Number Theory Seminar
room MATH 126
Reductions of Galois representations of small slopes
room MATH 126
Thu 12 Nov 2015, 3:30pm-4:30pm

Abstract

The reduction of the local Galois representation attached to an ordinary (slope 0) form at a prime p away from the level is well known to be reducible. In this talk we shall survey what is known about the reduction when the slope is small but positive.
 
We concentrate on the case of slope 1, which was treated essentially completely in recent joint work with S. Bhattacharya and S. Rozensztajn. We show that while the local reduction is essentially reducible, its exact shape depends on the congruence class of the weight mod p-1. Moreover, we show that in each such class there is a further congruence class of weights mod p where the local reduction is irreducible. We also distinguish between the so called peu and très ramifiée cases in the relevant non-semisimple reducible cases.
 
The proof uses the compatibility between the p-adic and mod p Local Langlands Correspondences with respect to the process of reduction. This reduces the computation to the automorphic side. We will try and explain most of the key ingredients used in the proof in a self-contained way.
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Thu 12 Nov 2015, 10:30pm
Math Education Research Reading
Math 126
"Effects of lecture instruction on student performance on qualitative questions"
Math 126
Thu 12 Nov 2015, 10:30pm-11:30am

Abstract

 
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UBC
Fri 13 Nov 2015, 12:00pm
Graduate Student Seminar
Math 103
Bifurcation Phenomena for an 1-D Nonlinear Schrodinger equation
Math 103
Fri 13 Nov 2015, 12:00pm-1:00pm

Abstract

I will first talk generally about quantum mechanics and the nonlinear Schrodinger equation. I will then turn my attention to the focusing
nonlinear Schrodinger equation which exhibits solitary wave solutions; the stability of which can be understood by studying the appropriate
linearization operator. I will say something about the interesting resonance eigenvalue that appears on the edge of the essential spectrum and
how it bifurcates.

Note for Attendees

 Pizza and pop will be provided.
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University of Texas at Austin
Mon 16 Nov 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Moduli Spaces of Microlocal Sheaves and Cluster Combinatorics
MATH 126
Mon 16 Nov 2015, 3:00pm-4:00pm

Abstract

We explore a relationship between combinatorics and certain moduli spaces appearing in symplectic geometry. The combinatorics comes from the theory of cluster algebras, a kind of unified theory of canonical bases in representation theory and algebraic geometry. Some basic features of cluster algebras are that they are defined from purely combinatorial data (for example, a quiver) and they are coordinate rings of varieties covered by algebraic tori with transition functions of a special, universal form. Despite the originally representation-theoretic motivation for the subject, connections between cluster theory and symplectic geometry emerged later through the appearance of similar formulae in wall-crossing and mirror symmetry.

We will discuss recent work expanding on this connection, in particular providing a universal framework for interpreting cluster varieties as moduli spaces of objects in Fukaya categories of Weinstein 4-manifolds. In simple examples these moduli spaces reduce to well-known ones, such as character varieties of surfaces and positroid cells in the Grassmannian. An accompanying theme, which plays a key role both technically and in relating the symplectic perspective to more standard representation-theoretic ones, is the role of categories of microlocal sheaves as topological counterparts of Fukaya categories. This is joint work with Vivek Shende, David Treumann, and Eric Zaslow.

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Camil Muscalu
Cornell University
Mon 16 Nov 2015, 4:00pm SPECIAL
Harmonic Analysis Seminar
Math Annex 1102
Multiple vector valued inequalities via the helicoidal method
Math Annex 1102
Mon 16 Nov 2015, 4:00pm-5:00pm

Abstract

 
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Department of Statistics at UBC
Tue 17 Nov 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Monte Carlo Methods for Complex Models
ESB 4133 (PIMS Lounge)
Tue 17 Nov 2015, 12:30pm-2:00pm

Abstract

Computational biology, spatio-temporal analysis, natural language processing and a range of other fields rely on increasingly complex probabilistic models to make predictions and take action. In practice, these models often need to incorporate high-dimensional latent variables, complex combinatorial spaces and various heterogeneous data-structures. Moreover, it is important to not only perform optimization on these models, but also to assess the uncertainty in predictions and reconstructions of latent states.

Monte Carlo methods have been used in the past several decades to approach these hard and important problems. Advances in probabilistic programming open the door for more widespread use of Monte Carlo, but computational efficiency remains a formidable challenge.

In this talk, I will provide some background on the state-of-the-art, and describe the progress that my collaborators and myself have been making towards more practical Monte Carlo methods. In particular, I describe Divide-and-Conquer Sequential Monte Carlo (D&C SMC), a method for performing inference on a collection of auxiliary distributions organized into a tree. In contrast to standard SMC samplers, D&C SMC exploits multiple populations of weighted particles, while still being an exact approximate method. D&C SMC is applicable to a broad class of probabilistic graphical models, including models with loops.

Note for Attendees

 Sushi lunch will be provided.
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Zachary Bradshaw
UBC Math
Tue 17 Nov 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Forward discretely self-similar solutions of the Navier-Stokes equations
ESB 2012
Tue 17 Nov 2015, 3:30pm-4:30pm

Abstract

For any discretely self-similar, incompressible initial data which is arbitrarily large in weak L^3, we construct a forward discretely self-similar solution to the 3D Navier-Stokes equations in the whole space. This also gives a third construction of self-similar solutions for any -1-homogeneous initial data in weak L^3,  improving those in by Jia-Sverak and Korobkov-Tsai for H\"older continuous data. Our method is based on a new, explicit a priori bound for the Leray equations. This is a joint work with Tai-Peng Tsai.
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Karen Yeats
SFU
Tue 17 Nov 2015, 4:00pm
Discrete Math Seminar
ESB 4127
A few c_2 invariants of circulant graphs
ESB 4127
Tue 17 Nov 2015, 4:00pm-5:00pm

Abstract

The c_2 invariant is an arithmetic graph invariant introduced by Brown and Schnetz in order to better understand Feynman integrals.  I will look at what can be said about the c_2 invariant of 4-regular circulant graphs with one vertex removed.  The answer is not much, but it's still interesting.  Yes, this is the same talk as I gave at SFU on October 6, so don't come expecting something new.
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Microsoft Research
Wed 18 Nov 2015, 3:00pm
Probability Seminar
ESB 2012
Random Games
ESB 2012
Wed 18 Nov 2015, 3:00pm-4:00pm

Abstract

Alice and Bob compete in a game of skill, making moves alternately until one or other reaches a winning position, at which the game ends.  Or, perhaps neither player can force a win, in which case optimal play continues forever, and we say that the game is drawn.

 

What is the outcome of a typical game?  That is, what happens if the game itself is chosen randomly, but is known to both players, who play optimally?

 

I will provide some answers (any many questions) in several settings, including trees, directed and undirected lattices, and point processes.  The competitive nature of game play frequently brings out some of the subtlest and most fundamental properties of probabilistic models.  We will encounter continuous and discontinuous phase transitions, hard-core models, probabilistic cellular automata, bootstrap percolation, maximum matching, and stable marriage.

 

Based on joint works with Riddhipratim Basu, Maria Deijfen, Irene Marcovici, James Martin and Johan Wastlund.

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Thu 19 Nov 2015, 10:30pm
Math Education Research Reading
Math126
"Investigating the secondary-tertiaty transition" by G. Geuedet
Math126
Thu 19 Nov 2015, 10:30pm-11:30am

Abstract

 
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Université de Montréal
Fri 20 Nov 2015, 2:00pm
Number Theory Seminar
room MATH 126
The Mahler measure of elliptic curves (note different day and time)
room MATH 126
Fri 20 Nov 2015, 2:00pm-3:00pm

Abstract

The Mahler measure of a multivariable polynomial P is given by the integral of log |P| where each of the variables moves on the unit circle and with respect to the Haar measure. In 1998 Boyd made a systematic numerical study of the Mahler measure of many polynomial families and found interesting conjectural relationships to special values of L-functions of elliptic curves. Recently, many of Boyd's conjectures have been proved by Burnault, Mellit, Rogers, and Zudilin. I will discuss some of those results and present new ones (in collaboration with D. Samart and W. Zudilin.)
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Tom Hutchcroft
UBC Math
Fri 20 Nov 2015, 3:00pm
Department Colloquium
MATX 1100
Circle Packing and Spanning Forests of Planar Graphs (Graduate Research Award Colloquium)
MATX 1100
Fri 20 Nov 2015, 3:00pm-4:00pm

Abstract

The Koebe-Andreev-Thurston Circle Packing Theorem lets us draw planar graphs in a canonical way, so that the geometry of the drawing reveals analytic properties of the graph. Circle packing has proven particularly effective in the study of random walks on planar graphs, where it allows us to estimate various quantities in terms of their counterparts for Brownian motion in the plane.

In this talk, I will introduce the theory of circle packing and discuss work with Asaf Nachmias in which we use circle packing to study uniform spanning forests of planar graphs, a probability model closely related to random walk. We prove that the free uniform spanning forest of any bounded degree, proper planar graph is connected almost surely, answering positively a question of Benjamini, Lyons, Peres and Schramm.

Our proof is quantitative, and also shows that uniform spanning forests exhibit some of the same behaviour universally for all bounded degree transient triangulations, provided that one measures distances and areas in the triangulation using the hyperbolic geometry of its circle packing rather than with the usual graph metric and counting measure.
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Cornell
Mon 23 Nov 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Matrix Factorizations for Complete Intersections
MATH 126
Mon 23 Nov 2015, 3:00pm-4:00pm

Abstract

The concept of basis of a vector space over a field generalizes to the concept of generators of a module over a ring. However, generators carry very little information about the structure of the module, in contrast to bases, which are very useful in the study of vector spaces. Hilbert introduced the approach to describe the structure of modules by free resolutions. Hilbert's Syzygy Theorem shows that minimal free resolutions over a polynomial ring are finite. By a result of Serre, it follows that most minimal free resolutions over quotient rings are infinite. We will discuss the structure of such resolutions. The concept of matrix factorization was introduced by Eisenbud 35 year ago, and it describes completely the asymptotic structure of minimal free resolutions over a hypersurface. Matrix factorizations have applications in many fields of mathematics: for the study of cluster algebras, Cohen-Macaulay modules, knot theory, moduli of curves,  quiver and group representations, and singularity theory.  Starting with Kapustin and Li, physicists discovered  amazing connections with string theory. In a current joint work with Eisenbud, we introduce the concept of matrix factorization for complete intersection rings and show that it suffices to describe the asymptotic structure of minimal free resolutions over complete intersections.
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Western University, Applied Mathematics
Mon 23 Nov 2015, 3:00pm
Institute of Applied Mathematics
ESB 2012
Optimal Residual and the Leaky Bucket
ESB 2012
Mon 23 Nov 2015, 3:00pm-4:00pm

Abstract

The numerical solution of ordinary differential equations is by now a very old subject. It's a surprise, therefore, that there's anything new to say about it at a basic level. This talk uses two very simple examples, the leaky bucket and the Dahlquist test problem, to demonstrate that there is indeed something new to say. This talk will be accessible to undergraduates. Joint work with Julia E. Jankowski, Yalçin Kaya, and Robert H.C. Moir. 

Note for Attendees

 Tea beforehand in the PIMS lounge
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Johnathan M. Bardsley
Professor of Mathematics, University of Montana
Tue 24 Nov 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Problems
ESB 4133 (PIMS Lounge)
Tue 24 Nov 2015, 12:30pm-1:30pm

Abstract

Many solution techniques for inverse problems involve solving an optimization problem using a numerical method. For example, the Tikhonov regularized solution is commonly defined as the minimizer of a penalized least squares function. Uncertainty quantification (UQ), on the other hand, often requires sampling from the Bayesian posterior density function arising from the assumed physical model, measurement error model, and prior probability density function. In this talk, we bring these two computational approaches (numerical methods and sampling) together and present posterior sampling – and specifically Markov Chain Monte Carlo (MCMC) – methods for UQ that utilize existing numerical algorithms for solving inverse problems. In all cases, care is taken to make sure that the MCMC methods presented provide theoretically correct samples from the posterior density function. Moreover, we present MCMC methods for both linear and nonlinear inverse problems.

Note for Attendees

Sushi lunch will be provided.
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Matthew Coles
UBC Math
Tue 24 Nov 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Resonance Eigenvalues and bound states of the Nonlinear Schroedinger Equation
ESB 2012
Tue 24 Nov 2015, 3:30pm-4:30pm

Abstract

There are many interesting questions concerning the Nonlinear Schroedinger Equation such as the existence and stability of solitary wave solutions as well as the long time behaviour of solutions. These problems are made more complicated by the presence of a resonance eigenvalue. Such occurrences are special cases which serve to worsen time decay estimates and complicate resolvent expansions. We will talk about some particular perturbation results whose treatment is non-standard since a relevant linear operator has a resonance.
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UBC Department of Computer Science
Tue 24 Nov 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Discrepancy theory and the Lovasz Local Lemma
ESB 4127
Tue 24 Nov 2015, 4:00pm-5:00pm

Abstract

Discrepancy theory has been an important research area in combinatorics and geometry for several decades. Recently there has been a lot of activity in discrepancy theory, in two directions. The first is efficient algorithmic proofs for classical discrepancy results that previously had only non-constructive proofs. The second is matrix generalizations of some classical discrepancy results, the canonical example of which is the solution of the Kadison-Singer conjecture by Marcus-Spielman-Srivastava (Polya Prize 2014).

In this talk I will give an overview of the field of discrepancy theory, then discuss a self-contained result of my own that uses the Lovasz Local Lemma to solve a discrepancy question that was overlooked for many years.

I will give a second talk on the Lovasz Local Lemma, focusing on algorithms, on Wednesday November 25th in the Probability Seminar.
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UBC Department of Computer Science
Wed 25 Nov 2015, 3:00pm
Probability Seminar
ESB 2012
An Algorithmic Proof of the Lovasz Local Lemma via Resampling Oracles
ESB 2012
Wed 25 Nov 2015, 3:00pm-4:00pm

Abstract

The Lovasz Local Lemma (LLL) is a seminal result in probabilistic combinatorics.  It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events.  Finding such an outcome by an efficient algorithm has been an active research topic for decades.  Breakthrough work of Moser and Tardos (2009) presented an efficient algorithm for a general setting primarily characterized by a product structure on the probability space.
 
In this work we present an efficient algorithm for a much more general setting.  Our main assumption is that there exist certain functions, called resampling oracles, that can be invoked to address the undesired occurrence of the events.  We show that, in all scenarios to which the original LLL applies, there exist resampling oracles; and for essentially all known applications of the LLL we have designed efficient resampling oracles.
 
Our analysis is based on an alternative view of the LLL using multivariate polynomials, due to Shearer (and Scott and Sokal). Probabilists have also studied this topic under the name of "1-dependent hard-core processes".
 
Joint work with Jan Vondrak (IBM Research).
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Thu 26 Nov 2015, 10:30am
Math Education Research Reading
Math126
"Mathematical Reasoning in Task Solving" by J. Lithner
Math126
Thu 26 Nov 2015, 10:30am-11:30am

Abstract

 
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Washington State University
Thu 26 Nov 2015, 3:30pm
Number Theory Seminar
room IRMACS 10901 (SFU)
The distribution of integral points on homogeneous varieties
room IRMACS 10901 (SFU)
Thu 26 Nov 2015, 3:30pm-4:30pm

Abstract

In this talk we will give a broad overview of the Linnik problems concerning the equidistribution of integral points on homogeneous varieties. One particular example concerns the Heegner points, which are roots in the complex upper-half plane of certain quadratic forms. We will discuss certain "sparse" equidistribution problems concerning these points and give an application of an analog of Linnik's famous theorem on the first prime in an arithmetic progression. This is joint work with Riad Masri and Matt Young.
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UBC
Fri 27 Nov 2015, 12:00pm
Graduate Student Seminar
Math 103
The Banach-Tarski paradox (an introduction to the theory of amenability)
Math 103
Fri 27 Nov 2015, 12:00pm-1:00pm

Abstract

 This week, I will talk about the famous Banach-Tarski paradox to give an brief introduction to the theory of amenability. The goal will be to give an intuition of "what does it means to be amenable, aside from having a mean ?"


This theory is not only great because it provides a field dedicated to making bad puns with "mean", "amen" or even "ramen", it also has a lot of interesting characterizations.

We will give a little overview of Banach-Tarski paradox to motivate the topic (and quickly re-attribute most of the result to Hausdorff), give a few alternative definitions and end up talking about graph theory.

Prerequisites : Be able to put up with my very average drawing skills, knowing how to pronounce Danish names always helps. Also, the axiom of choice is not optional, please don't be anti-choice axiom.

Note for Attendees

 Pizza and pop will be provided.
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UBC Math
Fri 27 Nov 2015, 3:00pm
Department Colloquium
MATX 1100
Pathway-centric modeling of microbial ecosystems (Graduate Research Award Colloquium)
MATX 1100
Fri 27 Nov 2015, 3:00pm-4:00pm

Abstract

New molecular techniques such as DNA sequencing provide conceptual insights into microbial community metabolism and biogeochemical cycling in natural and engineered ecosystems. However, attempts to mechanistically integrate molecular data with biogeochemistry are faced with the inhibitory complexity of individual cells and a large number of unknown physiological parameters. Recent work suggests that biochemical pathways are, at ecosystem scales, strongly shaped by thermodynamic and stoichiometric constraints. Pathway-centric mathematical theories rooted in fluxes of matter and energy could thus provide holistic insight into microbial ecosystems and global biogeochemical fluxes.

Oxygen minimum zones (OMZ) are oxygen-depleted regions in the ocean that are dominated by microbial metabolism, thus constituting ideal systems for developing theories of microbial ecology. I will present our current efforts to model the biogeochemistry of an intensely studied OMZ off the coast of Vancouver Island using reaction-advection-diffusion models. In contrast to conventional approaches, we focus on individual enzymes catalyzing metabolic pathways and assume that energy fluxes translate directly to gene expression and biosynthesis. We use DNA, mRNA and protein sequence data, as well as geochemical depth profiles and process rate measurements to calibrate and validate our models.
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Columbia
Mon 30 Nov 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Relative orbifold Donaldson-Thomas theory and local gerby curves
MATH 126
Mon 30 Nov 2015, 3:00pm-4:00pm

Abstract

In this talk I will introduce the generalization of relative Donaldson-Thomas theory to 3-dimensional smooth Deligne-Mumford stacks. We adopt Jun Li’s construction of expanded pairs and degenerations and prove an orbifold DT degeneration formula. I’ll also talk about the application in the case of local gerby curves, and its relationship to the work of Okounkov-Pandharipande and Maulik-Oblomkov.
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Kevin Henriot
Mathematics, UBC
Mon 30 Nov 2015, 3:00pm
Harmonic Analysis Seminar
MATX 1102
Diophantine equations and discrete restriction theory
MATX 1102
Mon 30 Nov 2015, 3:00pm-4:30pm

Abstract

In this two-part talk, we discuss a Fourier-analytic approach to solve translation-invariant systems of polynomial equations, when the variables lie in a dense subset of the integers. In the first part, we explain how discrete estimates in restriction theory come into play in this problem. In the second part, we show how to obtain weak restriction estimates by Bourgain's discrete version of the Tomas-Stein argument.
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