Seminars and Colloquia by Series

Linear series on metrized complexes of algebraic curves

Series
Algebra Seminar
Time
Monday, October 8, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matthew Baker – Georgia Tech
A metrized complex of algebraic curves over a field K is, roughly speaking, a finite edge-weighted graph G together with a collection of marked complete nonsingular algebraic curves C_v over K, one for each vertex; the marked points on C_v correspond to edges of G incident to v. We will present a Riemann-Roch theorem for metrized complexes of curves which generalizes both the classical and tropical Riemann-Roch theorems, together with a semicontinuity theorem for the behavior of the rank function under specialization of divisors from smooth curves to metrized complexes. The statement and proof of the latter result make use of Berkovich's theory of non-archimedean analytic spaces. As an application of the above considerations, we formulate a partial generalization of the Eisenbud-Harris theory of limit linear series to semistable curves which are not necessarily of compact type. This is joint work with Omid Amini.

Classification of minimal surfaces in $S^5$ with constant contact angle

Series
Geometry Topology Seminar
Time
Monday, October 8, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rodrigo Montes – Univerity of Curitiba, Brazil –
In this talk we introduce the notions of the contact angle and of the holomorphic angle for immersed surfaces in $S^{2n+1}$. We deduce formulas for the Laplacian and for the Gaussian curvature, and we will classify minimal surfaces in $S^5$ with the two angles constant. This classification gives a 2-parameter family of minimal flat tori of $S^5$. Also, we will give an alternative proof of the classification of minimal Legendrian surfaces in $S^5$ with constant Gaussian curvature. Finally, we will show some remarks and generalizations of this classification.

Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 8, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
005
Speaker
Xiaobing Feng – University of Tennessee
In this talk I shall present some latest advances on developing numerical methods (such as finite difference methods, Galerkin methods, discontinuous Galerkin methods) for fully nonlinear second order PDEs including Monge-Ampere type equations and Hamilton-Jacobi-Bellman equations. The focus of this talk is to present a new framework for constructing finite difference methods which can reliably approximate viscosity solutions of these fully nonlinear PDEs. The connection between this new framework with the well-known finite difference theory for first order fully nonlinear Hamilton-Jacobi equations will be explained. Extensions of these finite difference techniques to discontinuous Galerkin settings will also be discussed.

Braess's Paradox in Expanders

Series
Other Talks
Time
Monday, October 8, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Stephen Young – University of Louisville, Kentucky –
Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess¹s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess¹s paradox is ubiquitous in expander graphs. Specifically, we prove that Braess¹s paradox occurs in a large class of expander graphs with continuous convex latency functions. Our results extend previous work which held only when the graph was both denser and random and for random linear latency functions. We identify deterministic sufficient conditions for a graph with as few as a linear number of edges, such that Braess¹s Paradox almost always occurs, with respect to a general family of random latency functions. Joint work with Fan Chung and Wenbo Zhao. (* Note that this is an ARC/Theory Seminar and is in Klaus 1116W *)

Floquet bundles for tridiagonal competitive-cooperative systems

Series
CDSNS Colloquium
Time
Monday, October 8, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yi Wang – University of Sciences and Technology of China
For a general time-dependent linear competitive-cooperative tridiagonal system of differential equations, we obtain canonical Floquet invariant bundles which are exponentially separated in the framework of skew-product flows. The obtained Floquet theory is applied to study the dynamics on the hyperbolic omega-limit sets for the nonlinear competitive-cooperative tridiagonal systems in time-recurrent structures including almost periodicity and almost automorphy.

On the KLR conjecture in sparse random graphs

Series
Other Talks
Time
Friday, October 5, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
**Emory University**, Mathematics and Science Center, Rm W201
Speaker
Mathias Schacht – Math, University of Hamburg, Germany
(**This is at Emory and is a joint Emory - Georgia Tech Combinatorics Seminar. **) The KLR conjecture of Kohayakawa, Luczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G(n,p) satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. We prove a variant of this conjecture which is sufficient for most applications to random graphs. In particular, our result implies a number of recent probabilistic threshold results. We also discuss several further applications. This joint work with Conlon, Gowers, and Samotij.

An Introduction to Compressed Sensing

Series
ACO Student Seminar
Time
Friday, October 5, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ying Xiao – College of Computing, Georgia Tech
In the last 10 years, compressed sensing has arisen as an entirely new area of mathematics, combining ideas from convex programming, random matrices, theoretical computer science and many other fields. Candes (one of the originators of the area) recently spoke about two quite recent and exciting developments, but it might be interesting to revisit the fundamentals, and see where a lot of the ideas in the more recent works have developed. In this talk, I will discuss some of the earlier papers (Candes-Romberg-Tao), define the compressed sensing problem, the key restricted isometry property and how it relates to the Johnson-Lindenstrauss lemma for random projections. I'll also discuss some of the more TCS ideas such as compressed sensing through group testing, and hopefully some of the greedy algorithm ideas as well. Finally, if time allows, I'll draw parallels with other problems, such as matrix completion, phase retrieval etc. The talk will be quite elementary, requiring only a knowledge of linear algebra, and some probability.

Nanoengineered Surfaces: Transport Phenomena and Energy Applications

Series
Other Talks
Time
Friday, October 5, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
MRDC, Room 4211
Speaker
Evelyn Wang – Department of Mechanical Engineering, MIT

Please Note: Host: David Hu. Refreshments will be served. Speaker's Bio

Nanoengineered surfaces offer new possibilities to manipulate fluidic and thermal transport processes for a variety of applications including lab-on-a-chip, thermal management, and energy conversion systems. In particular, nanostructures on these surfaces can be harnessed to achieve superhydrophilicity and superhydrophobicity, as well as to control liquid spreading, droplet wetting, and bubble dynamics. In this talk, I will discuss fundamental studies of droplet and bubble behavior on nanoengineered surfaces, and the effect of such fluid-structure interactions on boiling and condensation heat transfer. Micro, nano, and hierarchical structured arrays were fabricated using various techniques to create superhydrophilic and superhydrophobic surfaces with unique transport properties. In pool boiling, a critical heat flux >200W/cm2 was achieved with a surface roughness of ~6. We developed a model that explains the role of surface roughness on critical heat flux enhancement, which shows good agreement with experiments. In dropwise condensation, we elucidated the importance of structure length scale and droplet nucleation density on achieving the desired droplet morphology for heat transfer enhancement. Accordingly, with functionalized copper oxide nanostructures, we demonstrated a 20% higher heat transfer coefficient compared to that of state-of-the-art dropwise condensing copper surfaces. These studies provide insights into the complex physical processes underlying fluid-nanostructure interactions. Furthermore, this work shows significant potential for the development and integration of nanoengineered surfaces to advance next generation thermal and energy systems.

Cramér type theorem for Wiener and Wigner stochastic integrals

Series
Stochastics Seminar
Time
Thursday, October 4, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
J.-C. Breton – Institut de Recherche Mathématique de Rennes
Cramér's theorem from 1936 states that the sum of two independent random variables is Gaussian if and only if these random variables are Gaussian. Since then, this property has been explored in different directions, such as for other distributions or non-commutative random variables. In this talk, we will investigate recent results in Gaussian chaoses and free chaoses. In particular, we will give a first positive Cramér type result in a free probability context.

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