Mathematics Dept.
  Events
Courant Institute, NYU
Fri 1 Dec 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--Microscopic description of Coulomb-type systems
ESB 2012
Fri 1 Dec 2017, 3:00pm-4:00pm

Abstract

 
 

Systems of points with Coulomb, logarithmic (or more generally inverse powers of the distance) interactions arise in various settings: an instance is the classical Coulomb gas which in some cases happens to be a random matrix ensemble, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems and its statistical mechanics. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given. This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.

The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Université Paris-Saclay
Fri 1 Dec 2017, 5:00pm SPECIAL
ESB 2012
UBC Mathematics Lecture Series: Regularized Optimal Transport. Part II
ESB 2012
Fri 1 Dec 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 second of a two part lecture. The first part will be given on Nov 30 2017, in ESB 2012 at the same time. Details for Part I are available here.
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Ping Xu (Penn State) and Hsuan-Yi Liao (Penn State)
Mon 4 Dec 2017, 3:00pm SPECIAL
MATH 126
Two Special Geometry Seminars
MATH 126
Mon 4 Dec 2017, 3:00pm-5:30pm

Details

Speaker: Ping Xu, Penn State
Time: 15:00-16:00 in MATH 126
Title: Formal exponential maps and L-infinity structures
Abstract: Exponential maps arise naturally in the contexts of Lie theory and smooth manifolds. The infinite jets of these classical exponential maps are related to the Poincare-Birkhoff-Witt isomorphism and the complete symbols of differential operators. We will investigate the question how to extend these maps to Z-graded manifolds by introducing formal exponential maps in a purely algebraic way. As an application, we will prove an analogue of a theorem of Kapranov in the dg manifold context: there is an L-infinity structure in connection with the Atiyah class of a dg manifold.

Speaker: Hsuan-Yi Liao, Penn State
Time: 16:15-17:15 in MATH 126
Title: A formality theorem for differential graded manifolds
Abstract: A dg (differential graded) manifold consists of a Z-graded manifold and a homological vector field. A wide range of geometric objects can be described in terms of dg manifolds, including Lie algebras, Lie algebroids, L-infintiy algebras and derived critical loci. We establish a formality theorem for finite-dimensional smooth dg manifolds: there is a "good” L-infinity quasi-isomorphism from the twisted dgla of polyvector fields to the twisted dgla of polydifferential operators. As an application, we prove the Kontsevich-Shoikhet conjecture: a Kontsevich-Duflo type theorem holds for all finite-dimensional smooth dg manifolds, which extends the classical Duflo theorem in Lie theory.
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Wenke Wilhelms
Department of Earth, Ocean and Atmospheric Sciences, UBC
Tue 5 Dec 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
A Mimetic Multiscale Method for Electromagnetic Simulations
ESB 4133 (PIMS Lounge)
Tue 5 Dec 2017, 12:30pm-1:30pm

Abstract

We develop a mimetic multiscale method to simulate quasi-static Maxwell's equations in frequency domain. This is especially useful for extensive geophysical models that include small-scale features. Applying the concept of multiscale methods, we avoid setting up a large and costly system of equations on the fine mesh where the material parameters are discretized on. Instead, we build and solve a system on a much coarser mesh. For doing that, it is inevitable to interpolate
between fine and coarse meshes. The construction of this coarse-to-fine interpolation is done by solving local optimization problems on each coarse cell incorporating the fine-mesh features. With our method being mimetic, the properties of the continuous differential operators are preserved in their discrete counterparts and thus, the resulting simulations do not contain spurious modes.


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Catherine Byrne
Wed 6 Dec 2017, 3:00pm
Mathematical Biology Seminar
PIMS Video-conference room
The Under-Representation of Women in Computational Biology
PIMS Video-conference room
Wed 6 Dec 2017, 3:00pm-4:00pm

Abstract

Gender equality is a major issue within science communities. While efforts to be proactive and bring awareness to gender inequality have been made in recent years, still only 1/8th of academic scientists are women. A recent paper published in PLOS Computational Biology (Hashe et al. 2017) highlights the under-representation of women in biology, computational biology, and computer science. Here, I will present their findings and lead a general discussion on women in science and ways we may help to close the gender gap.
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Stanford University
Mon 11 Dec 2017, 3:00pm
Department Colloquium
MATX 1100
Cobordism categories and moduli spaces of manifolds
MATX 1100
Mon 11 Dec 2017, 3:00pm-4:00pm

Abstract

Let M be a smooth manifold, let Diff(M) denote the topological group of sel-diffeomorphisms, and let BDiff(M) denote the "classifying space”. For any paracompact space X, there is a one-one correspondence between the set of homotopy classes [X, BDiff(M)] and the set of isomorphism classes of fibre bundles over X with fibre M. The classifying space BDiff(M) is referred to as the "moduli space of manifolds of type M". The study of the homotopy type of these spaces occupies a central place in smooth topology. 
 
In this talk I will discuss some contemporary approaches to studying the homotopy/homology of BDiff(M), for varying M. In particular I will discuss the results of Madsen and Weiss on the stable moduli spaces of Riemann surfaces and the results of Galatius and Randal-Williams on the stable moduli spaces of manifolds of dimension 2n. I will then present recent work of mine pertaining to the moduli spaces of odd dimensional manifolds, and manifolds with boundary, and discuss connections to cobordism categories and surgery theory.

Note for Attendees

Refreshments will be served in MATX 1100 at 2:30p.m. before this Mathematics Colloquium.
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Stanford University
Tue 12 Dec 2017, 3:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Parametrized morse theory, cobordism categories, and positive scalar curvature
ESB 4133 (PIMS Lounge)
Tue 12 Dec 2017, 3:00pm-4:00pm

Abstract

In this talk I will show how to use parametrized Morse theory to construct a map from the infinite loopspace of certain Thom spectrum, MTSpin(d), into the space of positive scalar curvature metrics on a closed spin manifold of dimension d > 4. My main novel construction is a cobordism category consisting of cobordisms equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. My first result identifies the homotopy type of the classifying space of this topological category with the infinite loopspace of another Thom spectrum related that is related to MTSpin(d), and built out of the space of Morse jets on Euclidean space. The result can viewed as an analogue of the well known theorem of Galatius, Madsen, Tillmann, and Weiss, for manifolds equipped with the extra geometric structure of a choice of admissible Morse function.

In the second part of the talk I will show how to use this cobordism category to probe the homotopy type of the space of positive scalar curvature metrics, R^{+}(M), on a closed, spin manifold M when dim(M) > 4. This uses a parametrized version of the Gromov-Lawson construction developed by Walsh and Chernysh. Our main result detects many non-trivial homotopy groups in the space of positive scalar curvature metrics R^{+}(M). It in particular gives an alternative proof and extension of a recent breakthrough theorem of Botvinnik, Ebert, and Randal-Williams.
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PhD Candidate: Xinyu Liu
Mathematics, UBC
Wed 13 Dec 2017, 12:30pm SPECIAL
Room 203, Graduate Student Centre, UBC
PhD Oral Exam: Schwartz Analysis and Intertwining Distributions
Room 203, Graduate Student Centre, UBC
Wed 13 Dec 2017, 12:30pm-2:30pm

Details

Abstract: In this dissertation, we combine the work of A. Aizenbud and D. Gourevitch on Schwartz functions on Nash manifolds, and the work of F. du Cloux on Schwartz inductions, to develop a toolbox of Schwartz analysis on algebraic groups. We then use these tools to study the intertwining operators between parabolic inductions, and the behaviour of intertwining distributions on certain open subsets. Finally we use our results to give new proof of results of F. Bruhat, on irreducibilities of degenerate principal series and minimal principal series.

Note for Attendees

Latecomers will not be admitted.
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Daphne Nesenberend
Wed 13 Dec 2017, 2:00pm
Mathematical Biology Seminar
ESB 5104
A continuous population level model of the co-operation of HIV and syphilis in the MSM population of Vancouver.
ESB 5104
Wed 13 Dec 2017, 2:00pm-3:00pm

Abstract

The HIV prevalence in the MSM population of Vancouver is slowly increasing,
but the amount of Syphilis cases is increasing very rapidly. Since Syphilis
facilitates the infection of HIV, there is a certain relation between the
infected populations. In this model, we explore the
co-operation of these two STD's and see what the influence of testing rate
is on the prevalence.
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Université de Sherbrooke
Wed 13 Dec 2017, 3:00pm
Department Colloquium
MATX 1100
A snapshot of Heegaard Floer theory
MATX 1100
Wed 13 Dec 2017, 3:00pm-4:00pm

Abstract

Heegaard Floer homology provides a suite of invariants for studying three-manifolds, introduced by Ozsváth and Szabó. This theory has, more recently, been expanded to treat manifolds with boundary through bordered Floer homology, providing the tools required to answer natural questions that arise when decomposing a three-manifold along a surface. This talk aims to provide a brief overview of Heegaard Floer theory, give a sense for some of the questions driving its study, and point to some recent progress on answering these.

Note for Attendees

Refreshments will be served in MATX 1100 at 2:30 p.m. before this Mathematics Colloquium.
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Université de Sherbrooke
Thu 14 Dec 2017, 3:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Heegaard Floer homology as immersed curves.
ESB 4133 (PIMS Lounge)
Thu 14 Dec 2017, 3:00pm-4:00pm

Abstract

The Heegaard Floer homology of a manifold with torus boundary can be expressed as a collection of immersed curves (possibly decorated with local systems). This provides a geometric structure theorem, interpreting the algebraic invariants that arise in bordered Floer homology. From this point of view, the Heegaard Floer homology of a closed manifold obtained by gluing manifolds (with boundary) along a torus may be recovered as the Lagrangian intersection Floer homology of the associated curves. In practice, this reduces gluing problems to simple minimal intersection counts. I'll set up this machinery and describe some of the applications that follow. This is joint work with Jonathan Hanselman and Jake Rasmussen.
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