McGill

Fri 28 Oct 2016, 11:10am
SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)

Nonpositive Immersions and Counting Cycles

ESB 4133 (PIMS Lounge)
Fri 28 Oct 2016, 11:10am12:10pm
Abstract
The "nonpositive immersion" property is a condition on a 2complex X that generalizes being a surface. When X has this property, its fundamental group appears to have has some very nice properties which I will discuss. I will spend the remainder of the talk outlining a proof that the nonpositive immersion property holds for a 2complex obtained by attaching a single 2cell to a graph. This was proven recently with Joseph Helfer and also independently by Lars Louder and Henry Wilton.
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McGill University

Fri 28 Oct 2016, 3:00pm
Department Colloquium
ESB 2012

CRMFieldsPIMS Award Lecture: The Cubical Route to Understanding Groups

ESB 2012
Fri 28 Oct 2016, 3:00pm4:00pm
Abstract
Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to rightangled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3manifolds, and simultaneously dramatically extended our understanding of many infinite groups.
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Yale University

Mon 31 Oct 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102

The torsion order of an algebraic variety

MATX 1102
Mon 31 Oct 2016, 3:00pm4:00pm
Abstract
The minimal multiple of the diagonal to admit a decomposition in the sense of Bloch and Srinivas is called the torsion order of a smooth projective variety. It is bounded above by the greatest common divisor of the degrees of all unirational parameterizations, and is a stable birational invariant. Recently, a degeneration method initiated by Voisin, and developed by ColliotThélène and Pirutka, has led to a breakthrough in establishing lower bounds for the torsion order, hence obstructions to stable rationality. The power of this method lies in its mix of inputs from algebraic cycles, Hodge theory, algebraic Ktheory, birational geometry, and singularity theory. I will survey the state of the art of this theory, which includes recent work of Chatzistamatiou and Levine, as well as provide some new examples.
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UBC

Mon 31 Oct 2016, 3:00pm
Harmonic Analysis Seminar
Math 126

Linear and trilinear Kakeyatype estimates in R^4

Math 126
Mon 31 Oct 2016, 3:00pm4:00pm
Abstract
A Besicovich set is a compact subset of R^d that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that every Besicovich set in R^d must have dimension d. I will discuss some new trilinear Kakeyatype bounds in R^4, and how these bounds can be used to obtain improved bounds on the dimension of certain sets in R^4 that resemble Kakeya sets. This is joint work with Larry Guth.
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Northwestern

Mon 31 Oct 2016, 4:15pm
Algebraic Geometry Seminar
MATX 1102

The derived MaurerCartan locus

MATX 1102
Mon 31 Oct 2016, 4:15pm5:15pm
Abstract
We give a new definition of the derived MaurerCartan locus MC^*(L), as a functor from differential graded Lie algebras to cosimplicial schemes, whose definition is sufficiently straightforward that it generalizes well to other settings such as analytic geometry. If L is differential graded Lie algebra, let L_+ be the truncation of L in positive degrees i>0. We prove that the differential graded algebra of functions on the cosimplicial scheme MC^*(L) is quasiisomorphic to the ChevalleyEilenberg complex of L_+, which is the usual definition of the derived MaurerCartan locus in characteristic zero.
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Sloan School of Management, MIT

Tue 1 Nov 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Mixedinteger convex optimization

ESB 4133 (PIMS Lounge)
Tue 1 Nov 2016, 12:30pm1:30pm
Abstract
Mixedinteger convex optimization problems are convex problems with the additional (nonconvex) constraints that some variables may take only integer values. Despite the past decades' advances in algorithms and technology for both mixedinteger *linear* and *continuous, convex* optimization, mixedinteger convex optimization problems have remained relatively more challenging and less widely used in practice. In this talk, we describe our recent algorithmic work on mixedinteger convex optimization which has yielded advances over the state of the art, including the globally optimal solution of open benchmark problems. Based on our developments, we have released Pajarito, an opensource solver written in Julia and accessible from popular optimization modeling frameworks. Pajarito is immediately useful for solving challenging mixed combinatorial continuous problems arising from engineering and statistical applications.
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University of Oregon

Tue 1 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Minimal hypersurfaces with free boundary and positive scalar curvature

ESB 2012
Tue 1 Nov 2016, 3:30pm4:30pm
Abstract
There is a wellknown technique due to SchoenYau from the late 70s which uses (stable) minimal hypersurfaces to find topological implications of a (closed) manifold's ability to support positive scalar curvature metrics. In this talk, we describe a version of this technique for manifolds with boundary and discuss how it can be used to study bordisms of positive scalar curvature metrics.
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University of California, San Diego

Wed 2 Nov 2016, 3:00pm
Probability Seminar
ESB 2012

Joint behavior of volume growth and entropy of random walks on groups

ESB 2012
Wed 2 Nov 2016, 3:00pm4:00pm
Abstract
In the last few years there has been significant advancement in understanding the possible range of behaviors of the volume growth and of the entropy and rate of escape of random walks on groups. Bartholdi and Erschler constructed the first family of intermediate growth groups whose volume growth function follows any prescribed nice enough function in the exponent range $[\alpha_0,1]$ for some explicit $\alpha_0 \approx 0.7674$. We discuss a variant of a construction of Kassabov and Pak which provides an alternative proof of the BartholdiErschler result. Different behaviors of entropy of random walks on these two families of groups allow us to deduce a result concerning possible joint behavior of intermediate volume growth and entropy of random walks within a certain range of parameters.
Joint with Gidi Amir.
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Note for Attendees