Mathematics Dept.
  Events
Stanford University
Tue 2 Jan 2018, 12:30pm SPECIAL
Department Colloquium
MATH 102 (special time, sushi will be served)
Stability in the homology of configuration spaces
MATH 102 (special time, sushi will be served)
Tue 2 Jan 2018, 12:30pm-1:30pm

Abstract

This talk will illustrate some patterns in the homology of the configuration space F_k(M), the space of ordered k-tuples 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 representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

Note special time. Sushi will be served.
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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, 12:00pm-1:00pm

Abstract

The Torelli subgroups of mapping class groups are fundamental objects in low-dimensional 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, 3:15pm-4:15pm

Abstract


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University of Lethbridge
Thu 4 Jan 2018, 3:30pm
Number Theory Seminar
TBA
TBA
TBA
Thu 4 Jan 2018, 3:30pm-10:00am

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, 3:30pm-5:00pm

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, non-smooth 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+1-k. 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, 9:00am-12:00pm

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, 1:00pm-4:00pm

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, 1:00pm-4:00pm

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, 3:00pm-4:00pm

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 Kontsevich-Zorich cocycle
ESB 4133 (PIMS Lounge)
Tue 9 Jan 2018, 3:00pm-4:00pm

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 non-trivial 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 Kontsevich-Zorich 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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Kevin Luli
UC-Davies
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, 3:30pm-4:30pm

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, 3:00pm-4:00pm

Abstract

 

Note for Attendees

There will be a reception before the talk in ESB 4133 (the PIMS lounge). This is a talk in the IAM/PIMS distinguished series.  
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TBA
Mon 15 Jan 2018, 4:00pm
Department Colloquium
MATH 100
TBA
MATH 100
Mon 15 Jan 2018, 4:00pm-5:00pm

Abstract


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Nicolau Sarquis Aiex
UBC & PIMS
Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Tue 16 Jan 2018, 3:30pm-4:30pm

Abstract

 
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TBA
Fri 19 Jan 2018, 3:00pm
Department Colloquium
ESB 2012
TBA
ESB 2012
Fri 19 Jan 2018, 3:00pm-4:00pm

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, 3:00pm-4:00pm

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.

Note for Attendees

Reception before the talk in ESB 4133 (the PIMS lounge). This is in the IAM/PIMS distinguished speaker series.
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Harvard
Thu 25 Jan 2018, 4:00pm SPECIAL
TBA
TBA
TBA
Thu 25 Jan 2018, 4:00pm-5:00pm

Details


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TBA
Fri 26 Jan 2018, 3:00pm
Department Colloquium
ESB 2012
TBA
ESB 2012
Fri 26 Jan 2018, 3:00pm-4:00pm

Abstract


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