Seminars and Colloquia by Series

Reconstruction Problems in Geometry

Series
Research Horizons Seminar
Time
Wednesday, September 3, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Dan MargalitGeorgia Tech Math Department
Here is a classical theorem. Consider a bijection (just a set map!) from the Euclidean plane to itself that takes 0 to 0 and takes the points on an arbitrary line to the points on a (possibly different line). The theorem is that such a bijection always comes from a linear map. I'll discuss various generalizations of this theorem in geometry, topology, and algebra, ending with a discussion of some recent, related research on the topology of surfaces.

A mathematical model of immune regulation: why we aren't all dead from autoimmune disease

Series
Mathematical Biology Seminar
Time
Wednesday, September 3, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James MooreSoM GaTech
The immune system must simultaneously mount a response against foreign antigens while tolerating self. How this happens is still unclear as many mechanisms of immune tolerance are antigen non-specific. Antigen specific immune cells called T-cells must first bind to Immunogenic Dendritic Cells (iDCs) before activating and proliferating. These iDCs present both self and foreign antigens during infection, so it is unclear how the immune response can be limited to primarily foreign reactive T-cells. Regulatory T-cells (Tregs) are known to play a key role in self-tolerance. Although they are antigen specific, they also act in an antigen non-specific manner by competing for space and growth factors as well as modifying DC behaviorto help kill or deactivate other T-cells. In prior models, the lack of antigen specific control has made simultaneous foreign-immunity and self-tolerance extremely unlikely. We include a heterogeneous DC population, in which different DCs present antigens at different levels. In addition, we include Tolerogenic DC (tDCs) which can delete self-reactive T-cells under normal physiological conditions. We compare different mathematical models of immune tolerance with and without Tregs and heterogenous antigen presentation.For each model, we compute the final number of foreign-reactive and self-reactive T-cells, under a variety of different situations.We find that even if iDCs present more self antigen than foreign antigen, the immune response will be primarily foreign-reactive as long as there is sufficient presentation of self antigen on tDCs. Tregs are required primarily for rare or cryptic self-antigens that do not appear frequently on tDCs. We also find that Tregs can onlybe effective when we include heterogenous antigen presentation, as this allows Tregs and T-cells of the same antigen-specificity to colocalize to the same set of DCs. Tregs better aid immune tolerance when they can both compete forspace and growth factors and directly eliminate other T-cells. Our results show the importance of the structure of the DC population in immune tolerance as well as the relative contribution of different cellular mechanisms.

Improved Approximation for Weighted Bipartite Edge Coloring

Series
Combinatorics Seminar
Time
Tuesday, September 2, 2014 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Arindam KhanGeorgia Tech
Weighted Bipartite Edge Coloring problem is a generalization of two classical optimization problems: Bipartite Edge Coloring and Bin Packing. Given an edge-weighted bipartite multi-graph G, the goal is to color all edges with minimum colors such that the sum of the edges incident to any vertex of any color is at most one. Chung and Ross conjectured that given an instance of the weighted bipartite edge coloring problem, there is a proper weighted coloring using at most 2n-1 colors where n denotes the maximum over all the vertices of the number of unit-sized bins needed to pack the weights of edges incident at the vertex. In this talk I will present an algorithm that gives a proper weighted coloring using $20n/9$ colors and improved results for some special cases. I will also present an alternative proof of Konig's edge coloring theorem using skew-supermodular functions. The talk will have all three components of ACO: Approximation Algorithms, Graph Theory and Supermodular Optimization.

Minors and dimension

Series
Graph Theory Seminar
Time
Thursday, August 28, 2014 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bartosz WalczakGT, Math and Jagiellonian University in Krakow
The dimension of a poset P is the minimum number of linear extensions of P whose intersection is equal to P. This parameter plays a similar role for posets as the chromatic number does for graphs. A lot of research has been carried out in order to understand when and why the dimension is bounded. There are constructions of posets with height 2 (but very dense cover graphs) or with planar cover graphs (but unbounded height) that have unbounded dimension. Streib and Trotter proved in 2012 that posets with bounded height and with planar cover graphs have bounded dimension. Recently, Joret et al. proved that the dimension is bounded for posets with bounded height whose cover graphs have bounded tree-width. My current work generalizes both these results, showing that the dimension is bounded for posets of bounded height whose cover graphs exclude a fixed (topological) minor. The proof is based on the Robertson-Seymour and Grohe-Marx structural decomposition theorems. I will survey results relating the dimension of a poset to structural properties of its cover graph and present some ideas behind the proof of the result on excluded minors.

Preparing for a career in academia

Series
Professional Development Seminar
Time
Wednesday, August 27, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Christine HeitschGeorgia Tech
The first meeting of our 2014-2015 professional development seminar for postdocs and other interested individuals (such as advanced graduate students). A discussion of the triumvirate of faculty positions: research, teaching, and service.

Transverse Surgery on Knots in Contact 3-Manifolds

Series
Geometry Topology Seminar
Time
Wednesday, August 27, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
James ConwayGeorgia Tech
We will define transverse surgery, and study its effects on open books, the Heegaard Floer contact invariant, and tightness. We show that surgery on the connected binding of a genus g open book that supports a tight contact structure preserves tightness if the surgery coefficient is greater than 2g-1. We also give criteria for when positive contact surgery on Legendrian knots will result in an overtwisted manifold.

How to Land a Job Outside of Academia

Series
Research Horizons Seminar
Time
Wednesday, August 27, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Matthew ClarkNorthrop Grumman, Future Technical Leaders (FTL) Program
Have you heard the urban legend that an experienced college recruiter can make an initial decision on whether or not to read your resume in less than six seconds? Would you like to see if your current resume can survive the six-second glance? Would you like to improve your chances of surviving the initial cut? Do you know what happens to your resume once you hand it to the recruiter? Should you have different resumes for online submission and handing to decision makers? How many different resumes should you prepare before you go to the career fair? Does it really take 30 revisions of your resume before it is ready to be submitted? Dr. Matthew Clark has supported college recruiting efforts for a variety of large corporations and is a master at sorting resumes in six seconds or under. Join us for a discussion of how most industry companies handle resumes, what types of follow up activities are worth-while, and, how to improve your chances of having your resume pass the “six second glance”.

Well posedness and decay for full Navier Stokes equations with temperature dependent coefficient

Series
PDE Seminar
Time
Tuesday, August 26, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Junxiong JiaGeorgia Tech
In this talk, firstly, we study the local and global well-posedness for full Navier-Stokes equations with temperature dependent coefficients in the framework of Besov space. We generalized R. Danchin's results for constant transport coefficients to obtain the local and global well-posedness for the initial with low regularity in Besov space framework. Secondly, we give a time decay rate results of the global solution in the Besov space framework which is not investigated before. Due to the low regularity assumption, we find that the high frequency part is also important for us to get the time decay.

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