Ecole Normale Supérieure de Lyon

Thu 27 Apr 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127

Iterated extensions and padic dynamical systems

ESB 4127
Thu 27 Apr 2017, 3:30pm5:00pm
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 padic field. Along the way, we'll see Coleman power series, padic dynamical systems and a little bit of padic 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 selfshrinking tori in R^4

Room 202, Anthropology and Sociology Bldg (ANSOC) 6303 NW Marine Drive, UBC
Mon 1 May 2017, 12:30pm2:30pm
Details
We prove that any sequence of conformally branched compact Lagrangian selfshrinkers 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 nondegeneracy the conformal structures. We also show that there is no branched immersion of Lagrangian selfshrinking sphere. When the area bound is small, we show that any such Lagrangian selfshrinking torus is embedded with uniform curvature estimates. For a general area bound, we prove that the entropy for the Lagrangian selfshrinking tori can only take finitely many values; this is done by deriving a LojasiewiczSimon type gradient inequality for the branched conformal selfshrinking 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 ColdingMinicozzi.
In the noncompact situation, we derive a parabolic OmoriYau maximum principle for a proper mean curvature flow when the ambient space has lower bound on lsectional 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 OmoriYau maximum principle for properly immersed selfshrinkers.
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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, 3:00pm4:00pm
Abstract
We present Possession Sketches, a new machine learning method for organizing and exploring a database of basketball playertracks. 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 topicmodeling 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 playertracking 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 playertracking data.
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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, 3:15pm4:15pm
Abstract
A saturated fusion system associated to a finite group G encodes the pstructure of the group as the Sylow psubgroup enriched with additional conjugation. The fusion system contains just the right amount of algebraic information to for instance reconstruct the pcompletion of BG, but not BG itself. Abstract saturated fusion systems F without ambient groups exist, and these have (pcompleted) 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 HopkinsKuhnRavenel 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, 3:15pm4:15pm
Abstract
Simplicial commutative rings are one of the first steps into "derived" rings that one can take. Many constructions for general E_inftyring spectra or even Zalgebras are simpler in the world of simplicial commutative rings; however, from a purely homotopytheoretic 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_inftyrings 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, 3:30pm4:30pm
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ETH Zürich

Fri 5 May 2017, 3:00pm
Number Theory Seminar
Math 126

TBA

Math 126
Fri 5 May 2017, 3:00pm4:30pm
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

LongTime Dynamics for the EnergyCritical Harmonic Map Heat Flow and Nonlinear Heat Equation

Room 202, Anthropology and Sociology Bldg. (ANSOC) 6306 NW Marine Drive, UBC
Tue 9 May 2017, 12:30pm2:30pm
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 longtime dynamics, stability and singularity formation, and the investigation of the role of special, solitonlike, solutions to the asymptotic behaviour of solutions.
Harmonic Map Heat Flow: We consider mcorotational 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 "concentrationcompactness plus rigidity" approach of Kenig and Merle and relies on the dissipation of the energy and a profile decomposition. We also treat mcorotational maps (m greater than 4) with nontrivial 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 finitetime blowup and show that the global solution asymptotically converges to a harmonic map.
Nonlinear Heat Equation: We also study solutions of the focusing energycritical 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, L2dissipation and an approximation argument. We then follow the "concentrationcompactness plus rigidity" roadmap of Kenig and Merle (and in particular the approach taken by Kenig and Koch for NavierStokes) to exclude finitetime blowup.
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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, 1:00pm2:00pm
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 padic geometry (details TBA)

Mon 15 May 2017, 11:00am1:00pm
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 padic 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: "padic etale cohomology of padic symmetric spaces"
Abstract: "We will present different ways to compute the padi etale cohomology
of layers of the Drinfeld tower, and give applications to the padic 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, 3:30pm4:30pm
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, 1:00pm2:00pm
Abstract
TBA
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UBC

Fri 10 Nov 2017, 3:00pm
SPECIAL
ESB 2012

PIMSUBC Distinguished ColloquiumTBA (for PIMS UBC Math Sciences prize)

ESB 2012
Fri 10 Nov 2017, 3:00pm4:00pm
Details
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Courant Institute, NYU

Fri 1 Dec 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMSUBC Distinguished ColloquiumTBA

ESB 2012
Fri 1 Dec 2017, 3:00pm4:00pm
Abstract
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SNS, Pisa

Fri 2 Mar 2018, 3:00pm
SPECIAL
Department Colloquium
ESB2012

PIMSUBC Distinguished ColloquiumTBA

ESB2012
Fri 2 Mar 2018, 3:00pm4:00pm
Abstract
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University of Oxford

Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012

PIMSUBC Distinguished ColloquiumTBA

ESB 2012
Fri 6 Apr 2018, 3:00pm4:00pm
Abstract
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Note for Attendees
Latecomers will not be admitted.