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 Events
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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Cédric Villani
Institut Henri Poincaré
Wed 3 May 2017, 3:00pm
PIMS Seminars and PDF Colloquiums
ESB 1013
Stability in some models of classical mathematical physics
ESB 1013
Wed 3 May 2017, 3:00pm-4:00pm

Abstract

Stability of classical mechanical systems is very old problem, still very much under scrutiny nowadays. Some techniques can be applied transversally in different problems.

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Cédric Villani is the Director of the Institut Henri Poincaré, France’s prime and oldest international institute for research in mathematical sciences. He has received many mathematical awards, including the Fields Medal in 2010, often considered the most prestigious in mathematics. Prof. Villani is a specialist of mathematical analysis applied to problems of statistical physics, geometry and probability. His books on gas theory and optimal transport theory have become classics.

 




Note for Attendees

Join us for refreshments from 2:45pm-3:00pm in ESB 4133.
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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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