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 Events
Ecole Normale Supérieure de Lyon
Thu 27 Apr 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Iterated extensions and p-adic dynamical systems
ESB 4127
Thu 27 Apr 2017, 3:30pm-5:00pm

Abstract

Let K be a field and let P be a polynomial. What can we say about the field generated by the roots of P and of all its iterates? I will discuss some questions motivated by this general problem when K is a p-adic field. Along the way, we'll see Coleman power series, p-adic dynamical systems and a little bit of p-adic Hodge theory.

(This talk is part of the PIMS focus semester on the mod p Langlands program).
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Ph.D. Candidate: Man Shun Ma
Mathematics, UBC
Mon 1 May 2017, 12:30pm SPECIAL
Room 202, Anthropology and Sociology Bldg (ANSOC) 6303 NW Marine Drive, UBC
Geometric properties of the space of Lagrangian self-shrinking tori in R^4
Room 202, Anthropology and Sociology Bldg (ANSOC) 6303 NW Marine Drive, UBC
Mon 1 May 2017, 12:30pm-2:30pm

Details

We prove that any sequence of conformally branched compact Lagrangian self-shrinkers in four dimensional Euclidean space with uniform area upper bound and fixed genus has a convergent subsequence, if the conformal structures do not degenerate. When the genus is one, we can drop the assumption on non-degeneracy the conformal structures. We also show that there is no branched immersion of Lagrangian self-shrinking sphere. When the area bound is small, we show that any such Lagrangian self-shrinking torus is embedded with uniform curvature estimates. For a general area bound, we prove that the entropy for the Lagrangian self-shrinking tori can only take finitely many values; this is done by deriving a Lojasiewicz-Simon type gradient inequality for the branched conformal self-shrinking tori.

Using the finiteness of entropy values, we construct a piecewise Lagrangian mean curvature flow for Lagrangian immersed tori, along which the Lagrangian condition is preserved, area is decreasing, and the compact type I singularities with a fixed area upper bound can be perturbed away in finitely many steps. This is a Lagrangian version of the construction for embedded surfaces by Colding-Minicozzi.

In the noncompact situation, we derive a parabolic Omori-Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on l-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in Euclidean spaces with uniform bounded second fundamental form. This generalizes a result of Wang for compact immersions. We also prove an Omori-Yau maximum principle for properly immersed self-shrinkers.

Note for Attendees

Latecomers will not be admitted.
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Statistics SFU
Mon 1 May 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Possession Sketches: Mapping NBA Strategies
ESB 2012
Mon 1 May 2017, 3:00pm-4:00pm

Abstract

We present Possession Sketches, a new machine learning method for organizing and exploring a database of basketball player-tracks. Our method organizes basketball possessions by offensive structure. We first develop a model for populating a dictionary of short, repeated, and spatially registered actions. Each action corresponds to an interpretable type of player movement. We examine statistical patterns in these actions, and show how they can be used to describe individual player behavior. Leveraging this vocabulary of actions, we develop a hierarchical model that describes interactions between players. Our approach draws on the topic-modeling literature, extending Latent Dirichlet Allocation (LDA) through a novel representation of player movement data which uses techniques common in animation and video game design. We show that our model is able to group together possessions with similar offensive structure, allowing for efficient search and exploration of the entire database of player-tracking data. We show that our model finds repeated offensive structure in teams (e.g. strategy), providing a much more sophisticated, yet interpretable lens into basketball player-tracking data.

Note for Attendees

 This is a talk in the BC Data Colloquium. Reception beforehand in ESB 4133 (the PIMS lounge).
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MIT
Wed 3 May 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Character maps, free loops, and fusion systems
ESB 4133 (PIMS Lounge)
Wed 3 May 2017, 3:15pm-4:15pm

Abstract

A saturated fusion system associated to a finite group G encodes the p-structure of the group as the Sylow p-subgroup enriched with additional conjugation. The fusion system contains just the right amount of algebraic information to for instance reconstruct the p-completion of BG, but not BG itself. Abstract saturated fusion systems F without ambient groups exist, and these have (p-completed) classifying spaces BF as well.

In a joint project with Tomer Schlank and Nat Stapleton, we combine the theory of abstract fusion systems with the work by Hopkins-Kuhn-Ravenel and Stapleton on transchromatic character maps, and we generalize several results from finite groups to fusion systems.

A main ingredient of this project is studying the free loop spaces L(BG) and L(BF) for groups and fusion systems, and constructing transfer maps from L(BG) to L(BH) when H is a subgroup of G.
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Harvard University
Thu 4 May 2017, 3:15pm SPECIAL
Topology and related seminars
Nonconnective simplicial commutative rings
Thu 4 May 2017, 3:15pm-4:15pm

Abstract

 Simplicial commutative rings are one of the first steps into "derived" rings that one can take. Many constructions for general E_infty-ring spectra or even Z-algebras are simpler in the world of simplicial commutative rings; however, from a purely homotopy-theoretic or categorical picture they are slightly mysterious. I will explain ongoing work with Bhargav Bhatt on an extended theory of "generalized rings" which extends this category to allow nonconnective objects. Many "equational" constructions which cannot work with E_infty-rings extend well to generalized rings.
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Ecole Normale Supérieure de Lyon
Thu 4 May 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
TBA
ESB 4127
Thu 4 May 2017, 3:30pm-4:30pm

Abstract

TBA

(This talk is part of the PIMS focus semester on the mod p Langlands program).
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ETH Zürich
Fri 5 May 2017, 3:00pm
Number Theory Seminar
Math 126
TBA
Math 126
Fri 5 May 2017, 3:00pm-4:30pm

Abstract

TBA
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Ph.D. Candidate: Dimitrios Roxanas
Mathematics, UBC
Tue 9 May 2017, 12:30pm SPECIAL
Room 202, Anthropology and Sociology Bldg. (ANSOC) 6306 NW Marine Drive, UBC
Long-Time Dynamics for the Energy-Critical Harmonic Map Heat Flow and Nonlinear Heat Equation
Room 202, Anthropology and Sociology Bldg. (ANSOC) 6306 NW Marine Drive, UBC
Tue 9 May 2017, 12:30pm-2:30pm

Details

The emphasis of this thesis is on critical parabolic problems, in particular, the harmonic map heat from the plane to S2, and nonlinear focusing heat equations with an algebraic nonlinearity.

The focus of this work has been on long-time dynamics, stability and singularity formation, and the investigation of the role of special, soliton-like, solutions to the asymptotic behaviour of solutions.

Harmonic Map Heat Flow: We consider m-corotational solutions to the harmonic map heat flow from R2 to S2. We first work in a class of maps with trivial topology and energy of the initial data below two times the energy of the stationary harmonic map solutions. We give a new proof of global existence and decay. The proof is based on the "concentration-compactness plus rigidity" approach of Kenig and Merle and relies on the dissipation of the energy and a profile decomposition. We also treat m-corotational maps (m greater than 4) with non-trivial topology and energy of the initial data less than three times the energy of the stationary harmonic map solutions. Through a new stability argument we rule out finite-time blow-up and show that the global solution asymptotically converges to a harmonic map.

Nonlinear Heat Equation: We also study solutions of the focusing energy-critical nonlinear heat equation. We show that solutions emanating from initial data with energy and kinetic energy below those of the stationary solutions are global and decay to zero. To prove that global solutions dissipate to zero we rely on a refined small data theory, L2-dissipation and an approximation argument. We then follow the "concentration-compactness plus rigidity" roadmap of Kenig and Merle (and in particular the approach taken by Kenig and Koch for Navier-Stokes) to exclude finite-time blow-up.

Note for Attendees

Latecomers will not be admitted.
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Université de Montpellier, France
Fri 12 May 2017, 1:00pm
Diff. Geom, Math. Phys., PDE Seminar
Time and Location TBA
Prescribing the curvature of hyperbolic convex bodies
Time and Location TBA
Fri 12 May 2017, 1:00pm-2:00pm

Abstract

 The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure \mu , Alexandrov problem consists in proving the existence of a convex body whose curvature measure is \mu . In the Euclidean space, this problem is equivalent to an optimal transport problem on the sphere.
 
In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain how to relate this problem to a non linear Kantorovich problem on the sphere and how to solve it.
 
Joint work with J\’er\^ome Bertrand.
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Pierre Colmez, Wieslawa Niziol, and others
Mon 15 May 2017, 11:00am
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
Week of May 15 - Lectures on p-adic geometry (details TBA)
Mon 15 May 2017, 11:00am-1:00pm

Abstract

During the week of May 15 through May 19 there will be lectures by several visitors as part of the PIMS focus period on Representations in Arithmetic, on the topics in p-adic geometry related to Scholze's work on perfectoid spaces. This listing is a placeholder until there's a specific schedule set for the talks.

The talks by Colmez and Niziol will have the following title and abstract:
Title: "p-adic etale cohomology of p-adic symmetric spaces"
Abstract: "We will present different ways to compute the p-adi etale cohomology
of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence".


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University of Toronto
Thu 25 May 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
TBA
ESB 4127
Thu 25 May 2017, 3:30pm-4:30pm

Abstract

 
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Yale University
Mon 29 May 2017, 1:00pm SPECIAL
Department Colloquium
Math Annex 1100
Niven Lecture: title TBA
Math Annex 1100
Mon 29 May 2017, 1:00pm-2:00pm

Abstract

TBA

Note for Attendees


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Yaniv Plan
UBC
Fri 10 Nov 2017, 3:00pm SPECIAL
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA (for PIMS UBC Math Sciences prize)
ESB 2012
Fri 10 Nov 2017, 3:00pm-4:00pm

Details

 
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Syvia Serfaty
Courant Institute, NYU
Fri 1 Dec 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 1 Dec 2017, 3:00pm-4:00pm

Abstract

 
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Umberto Zannier
SNS, Pisa
Fri 2 Mar 2018, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--TBA
ESB2012
Fri 2 Mar 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
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University of Oxford
Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 6 Apr 2018, 3:00pm-4:00pm

Abstract

 
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