Stanford University

Tue 2 Jan 2018, 12:30pm
SPECIAL
Department Colloquium
MATH 102 (special time, lunch will be served)

Stability in the homology of configuration spaces

MATH 102 (special time, lunch will be served)
Tue 2 Jan 2018, 12:30pm1:30pm
Abstract
This talk will illustrate some patterns in the homology of the configuration space F_k(M), the space of ordered ktuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representationtheoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higherorder stability phenomena  relationships between unstable homology classes in different degrees  established in recent work joint with Jeremy Miller. This project was inspired by workinprogress of GalatiusKupersRandalWilliams.
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Stanford University

Wed 3 Jan 2018, 12:00pm
SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)

Stability in the homology of Torelli groups

ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 12:00pm1:00pm
Abstract
The Torelli subgroups of mapping class groups are fundamental objects in lowdimensional topology, through some basic questions about their structure remain open. In this talk I will describe these groups, and how to use tools from representation theory to establish patterns their homology. This project is joint with Jeremy Miller and Peter Patzt. These "representation stability" results are an application of advances in a general algebraic framework for studying sequences of group representations.
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University of Adelaide

Wed 3 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

TBA (provisional time slot)

ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 3:15pm4:15pm
Abstract
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University of Lethbridge

Thu 4 Jan 2018, 3:30pm
Number Theory Seminar
TBA

TBA

TBA
Thu 4 Jan 2018, 3:30pm10:00am
Abstract
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University of Toronto

Thu 4 Jan 2018, 3:30pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
TBA

Free Discontinuities in Optimal Transport

TBA
Thu 4 Jan 2018, 3:30pm5:00pm
Abstract
Optimal maps in R^n to disconnected targets necessarily contain discontinuities (i.e.~tears). But how smooth are these tears? When the target components are suitably separated by hyperplanes, nonsmooth versions of the implicit function theorem can be developed which show the tears are hypersurfaces given as differences of convex functions  DC for short. If in addition the targets are convex the tears are actually C^{1,\alpha}. Similarly, under suitable affine independence assumptions, singularities of multiplicity k lie on DC rectifiable submanifolds of dimension n+1k. These are stable with respect to W_\infty perturbations of the target measure. Moreover, there is at most one singularity of multiplicity n. This represents joint work with Jun Kitagawa.
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Sat 6 Jan 2018, 9:00am
SPECIAL
MATH 126

Qualifying Exams  Analysis

MATH 126
Sat 6 Jan 2018, 9:00am12:00pm
Details
For more information on Qualifying Exams, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
Lunch will be provided for students writing the Analysis exam.
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Sat 6 Jan 2018, 1:00pm
SPECIAL
MATH 126

Qualifying Exams  Algebra

MATH 126
Sat 6 Jan 2018, 1:00pm4:00pm
Details
For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
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Sat 6 Jan 2018, 1:00pm
SPECIAL
MATH 126

Qualifying Exams  Differential Equations

MATH 126
Sat 6 Jan 2018, 1:00pm4:00pm
Details
For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
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Stanford University

Mon 8 Jan 2018, 3:00pm
Department Colloquium
ESB 2012 (note special time)

Dynamics, geometry, and the moduli space of Riemann surfaces

ESB 2012 (note special time)
Mon 8 Jan 2018, 3:00pm4:00pm
Abstract
The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.
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Stanford University

Tue 9 Jan 2018, 3:00pm
SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)

Totally geodesic submanifolds of Teichmuller space and the KontsevichZorich cocycle

ESB 4133 (PIMS Lounge)
Tue 9 Jan 2018, 3:00pm4:00pm
Abstract
One of the ways we understand Teichmuller space, endowed with the Teichmuller metric, is by studying Teichmuller discs. They exist in great abundance: There is a Teichmuller disc through any point and in any direction. Typically, their projection to moduli space is dense, and yet infinitely often their projection is a closed subvariety of moduli space called a Teichmuller curve. Recently, in joint work with Eskin, McMullen, and Mukamel, we discovered the first nontrivial examples of higher dimensional analogues of Teichmuller discs, namely totally geodesic submanifolds.
In this talk, we will explain that such higher dimensional totally geodesic submanifolds are much more rigid and rare than Teichmuller discs: Each must cover a closed subvariety of moduli space, and only finitely many such subvarieties exist in each moduli space. This result is an application of joint work with Eskin and Filip on the KontsevichZorich cocycle. One of the goals of the talk will be to explain what this cocycle is and why it lies at the heart of Teichmuller dynamics.
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UCDavies

Tue 9 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Variational Problems on Arbitrary Sets

ESB 2012
Tue 9 Jan 2018, 3:30pm4:30pm
Abstract
Let E be an arbitrary subset of R^n. Given real valued functions f defined on E and g defined on R^n, the classical obstacle problem asks for a minimizer of the Dirichlet energy subject to the following two constraints: (1) F = f on E and (2) F lies above g on R^n. In this talk, we will discuss how to use extension theory to construct (almost) solutions directly. We will also explain several recent results that will help lay the foundation for building a complete theory revolving around the belief that any variational problems that can be solved using PDE theory can also be dealt with using extension theory.
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Cornell Physics and Mechanical & Aerospace Engineering

Mon 15 Jan 2018, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

From Newton's Law to Neurons

ESB 2012
Mon 15 Jan 2018, 3:00pm4:00pm
Abstract
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Mon 15 Jan 2018, 4:00pm
Department Colloquium
MATH 100

TBA

MATH 100
Mon 15 Jan 2018, 4:00pm5:00pm
Abstract
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UBC & PIMS

Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar


Tue 16 Jan 2018, 3:30pm4:30pm
Abstract
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Fri 19 Jan 2018, 3:00pm
Department Colloquium
ESB 2012

TBA

ESB 2012
Fri 19 Jan 2018, 3:00pm4:00pm
Abstract
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Cornell Statistical Science and Biological Statistics & Computational Biology

Mon 22 Jan 2018, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

An ODE to Statistics: Inference about Nonlinear Dynamics

ESB 2012
Mon 22 Jan 2018, 3:00pm4:00pm
Abstract
Ordinary differential equation models are used extensively within mathematics as descriptions of processes in the real world. However, they are rarely employed by statisticians and there is a paucity of methods for combining differential equation models with data. This talk provides a survey of recently developed statistical methods for estimating parameters from data, conducting model criticism and improvement for differential equation models in the light of data, and designing experiments that yield optimal estimates of parameters. It ends with some perspectives on the current state of the field and open problems.
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Harvard

Thu 25 Jan 2018, 4:00pm
SPECIAL
TBA

TBA

TBA
Thu 25 Jan 2018, 4:00pm5:00pm
Details
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Fri 26 Jan 2018, 3:00pm
Department Colloquium
ESB 2012

TBA

ESB 2012
Fri 26 Jan 2018, 3:00pm4:00pm
Abstract
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Note for Attendees
Note special time. Lunch will be served.