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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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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Seminar Information Pages

Note for Attendees
Latecomers will not be admitted.