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Series: Other Talks

Series: Other Talks

The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions:

- The University of Alabama at Birmingham
- The Georgia Institute of Technology
- Emory University
- The University of Tennessee Knoxville

The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology.

- Natasa Sesum (U Penn)
- Alexandru Ionescu (U Wisconsin)
- Sergiu Klainerman (Princeton U)
- Alex Freire (U Tennessee Knoxville)
- Christian Hainzl (UAB)

A poster session will be hosted. There will also be an evening public lecture by plenary speaker Sergiu Klainerman entitled The Mathematical Magic of Black Holes.

Series: Other Talks

Leo Chen: The Shape and Stability of a Flexible Sheet in a von Karman Vortex Street

Michelle Delcourt: Dessin and Manturov bracket shuffles

In this talk we will explore the connections between knot theory and combinatorics. Links are related to Grothendieck's dessins d'enfants. Cartographic one-vertex dessins can be represented by chord diagrams. The diagrams can be recorded as "words" using a finite alphabet (k-bracket parenthesis system). Many combinatorial objects are related to these Manturov bracket structures.

Series: Other Talks

We will present a sheaf-theoretic proof of the Riemann-Roch theorem
for projective nonsingular curves.

Series: Other Talks

We will state Serre's fundamental finiteness and vanishing results for the cohomology
of coherent sheaves on a projective algebraic variety. As an application, we'll prove that the
constant term of the Hilbert Polynomial does not depend on the projective embedding, a fact which
is hard to understand using classical (non-cohomological) methods.

Series: Other Talks

In the 60s, Grothendieck had the remarkable idea of introducing a new kind of topology where open coverings of X are no longer collections of subsets of X, but rather certain maps from other spaces to X. I will give some examples to show why this is reasonable and what one can do with it.

Series: Other Talks

We will show that the construction of derived functors satisfy the required universal property.I will then show that, for any ringed space, the abelian category of all sheaves of Modules has enough injectives. We achieve this by first characterizing injective abelian groups (Baer's theorem).The relation with Cech cohomology will also be studied. In particular, I will show that the first Cech and Grothendieck sheaf cohomology groups are isomorphic for any topological space (without using spectral sequences).

Series: Other Talks

We consider the Stochastic Differential Equation
$dX_\epsilon=b(X_\epsilon)dt + \epsilon dW$ . Given a domain D, we
study how the exit time and the distribution of the process at the time
it exits D behave as \epsilon goes to 0. In particular, we cover the
case in which the unperturbed system $\frac{d}{dt}x=b(x)$ has a unique
fixed point of the hyperbolic type. We will illustrate how the behavior
of the system is in the linear case. We will remark how our results
give improvements to the study of systems admitting heteroclinic or
homoclinic connections. We will outline the general proof in two
dimensions that requires normal form theory from differential
equations. For higher dimensions, we introduce a new kind of non-smooth
stochastic calculus.

Series: Other Talks

We will continue the study of derived functors between abelian categories. I will show why injective objects are needed for the construction. I will then show that, for any ringed space, the abelian category of all sheaves of Modules has enough injectives. The relation with Cech cohomology will also be studied.

Joint ACO/DOS - Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions

Series: Other Talks

Organizer: Daniel Dadush, ACO Student, ISyE

Applications in complex systems such as the Internet have spawned recent interest in studying situations involving multiple agents with their individual cost or utility functions. We introduce an algorithmic framework for studying combinatorial problems in the presence of multiple agents with submodular cost functions. We study several fundamental covering problems (Vertex Cover, Shortest Path, Perfect Matching, and Spanning Tree) in this setting and establish tight upper and lower bounds for the approximability of these problems. This talk is based on joint work with Gagan Goel, Chinmay Karande and Wang Lei. This is a joint ACO/DOS seminar, so please come a little early for pizza and refreshments sponsored by ACO.