| Talk_id | Date | Speaker | Title |
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18596
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Thursday 9/5
4:10 PM
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Eric Zaslow, Northwestern University
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Applications of Constructible Sheaves to Symplectic Topology
- Eric Zaslow, Northwestern University
- Applications of Constructible Sheaves to Symplectic Topology
- 09/05/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
My goal is to explain a few applications of constructible sheaves to symplectic topology through examples that we can calculate together on the board.
In particular, I would like to explain how sheaves relate to: 1) Legendrian knot invariants, 2) cluster varieties, 3) nonfillability results for Legendrian surfaces.
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18587
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Thursday 9/19
4:10 PM
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Aaron Naber, Northwestern University
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Introduction to the Energy Identity for Yang-Mills
- Aaron Naber, Northwestern University
- Introduction to the Energy Identity for Yang-Mills
- 09/19/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
In this talk we give an introduction to the analysis of the Yang-Mills equation in higher dimensions. In particular, when studying sequences of solutions we will study the manner in which blow up can occur, and how this blow up may be understood through the classical notions of the defect measure and bubbles. The energy identity is an explicit conjectural relationship relating the energy density of the defect measure at a point to the bubbles which occur at that point. This talk is introductory and we will spend most of our time understanding the words of this abstract. If time permits we will briefly discuss the ideas needed to prove this conjecture and the related $W^{2,1}$-conjecture. The work is joint with Daniele Valtorta.
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18597
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Thursday 10/10
4:10 PM
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Romyar Sharifi, UCLA
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Modular symbols and the arithmetic of cyclotomic fields
- Romyar Sharifi, UCLA
- Modular symbols and the arithmetic of cyclotomic fields
- 10/10/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
The arithmetic of cyclotomic fields, and the structure of their class groups, has been studied since the time of Kummer in connection with Fermat’s Last Theorem. The work of Ribet in 1976 uncovered a subtle influence of the geometry of modular curves on this structure. I’ll discuss how this connection goes even deeper and define a surprisingly explicit map from the homology group of a modular curve to a K-group related to the class group of a cyclotomic field. I’ll then indicate how this is turning out to be just one instance of a more general phenomenon, touching briefly on joint work with Takako Fukaya and Kazuya Kato and separate joint work with Akshay Venkatesh.
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18588
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Thursday 10/17
4:10 PM
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Frank Sottile, Texas A&M University
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Higher convexity for complements of tropical objects
- Frank Sottile, Texas A&M University
- Higher convexity for complements of tropical objects
- 10/17/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
Gromov generalized the notion of convexity for open subsets
of $\mathbf{R}^n$ with hypersurface boundary, defining $k$-convexity, or
higher convexity and Henriques applied the same notion to
complements of amoebas. He conjectured that the complement
of an amoeba of a variety of codimension $k+1$ is $k$-convex.
I will discuss work with Mounir Nisse in which we study the
higher convexity of complements of coamoebas and of tropical
varieties, proving Henriques' conjecture for coamoebas and
establishing a form of Henriques' conjecture for tropical varieties in some cases.
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18600
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Thursday 10/24
4:10 PM
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Robin Graham, University of Washington
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Geodesic X-ray Transforms and Boundary Rigidity
- Robin Graham, University of Washington
- Geodesic X-ray Transforms and Boundary Rigidity
- 10/24/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
This talk will introduce the problem of injectivity and
inversion of geodesic X-ray transforms in various geometric settings. The
associated nonlinear boundary rigidity problem, which consists of
determining a Riemannian metric on a compact manifold-with-boundary from
the lengths of its geodesics joining boundary points, will also be
discussed. Classical results and recent progess will be described,
including current research on the analogous questions in the setting of
asymptotically hyperbolic manifolds.
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18589
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Thursday 10/31
4:10 PM
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Robert Pego, Carnegie Mellon University
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Dynamics in models of coagulation and fragmentation
- Robert Pego, Carnegie Mellon University
- Dynamics in models of coagulation and fragmentation
- 10/31/2019
- 4:10 PM - 5:00 PM
- C304 Wells Hall
Coaglation-fragmentation equations are simple, nonlocal models for evolution of the size distribution of clusters, appearing widely in science and technology. But few general analytical results characterize their dynamics. Solutions can exhibit self-similar growth, singular mass transport, and weak or slow approach to equilibrium. I will review some recent results in this vein, discussing: the cutoff phenomenon (as in card shuffling) for Becker-Doering equilibration; stationary and spreading profiles in a data-driven model of fish school size; and temporal oscillations recently found in models lacking detailed balance. A special role is played by Bernstein transforms and complex function theory for Pick or Herglotz functions.
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