Seminars and Colloquia by Series

Thursday, March 27, 2014 - 12:00 , Location: Skiles 006 , Gagik Amirkhanyan , Georgia Tech , gagik@math.gatech.edu , Organizer:
The talk consists of two parts.The first part is devoted to results in Discrepancy Theory. We consider geometric discrepancy in higher dimensions (d > 2) and obtain estimates in Exponential Orlicz Spaces.  We establish a series of dichotomy-type results for the discrepancy function which state that if the $L^1$ norm of the discrepancy function is too small (smaller than the conjectural bound), then the discrepancy function has to be very large in some other function space.The second part of the thesis is devoted to results in Additive Combinatorics. For a set with small doubling an order-preserving Freiman 2-isomorphism is constructed which maps the set to a dense subset of an interval. We also present several applications.
Friday, March 14, 2014 - 10:30 , Location: Skiles 005 , Rebecca R. Winarski , Georgia Tech , Organizer:
We say that a cover of surfaces S-> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the group of deck transformations.  We identify one necessary condition and one sufficient condition for when a cover has this property.  We give new explicit examples of irregular branched covers that do not satisfy the necessary condition as well as explicit covers that satisfy the sufficient condition.  Our criteria are conditions on simple closed curves, and our proofs use the combinatorial topology of curves on surfaces.
Thursday, October 10, 2013 - 12:00 , Location: Skiles 170 , Meredith Casey , Georgia Tech , Organizer:
Friday, June 21, 2013 - 10:00 , Location: Skiles 005 , Farbod Shokrieh , School of Mathematics, Georgia Tech , Organizer:

Advisor: Dr. Matthew Baker

We study various binomial and monomial ideals related to the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe minimal polyhedral cellular free resolutions for these ideals. We will show that the resolutions of all these ideals are closely related and that their Betti tables coincide. As corollaries we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related in the theory of chip-firing games on graphs -- including Merino's proof of Biggs' conjecture and Baker-Shokrieh's characterization of reduced divisors in terms of potential theory -- also follow immediately from our general techniques and results.
Monday, April 29, 2013 - 15:00 , Location: Skiles 005 , Jingfang Liu , School of Mathematics, Georgia Tech , Organizer: Haomin Zhou
Thursday, April 25, 2013 - 13:30 , Location: Skiles 005 , Ke Yin , School of Mathematics, Georgia Tech , Organizer: Haomin Zhou
Tuesday, March 26, 2013 - 16:00 , Location: Skiles 005 , Kai Ni , School of Mathematics, Georgia Tech , Organizer:
Tuesday, February 5, 2013 - 15:00 , Location: Skiles 005 , James Scurry , Georgia Tech , Organizer:
Tuesday, December 4, 2012 - 15:00 , Location: Skiles 005 , Huijun Feng , School of Mathematics, Georgia Tech , Organizer: Liang Peng
Monday, November 5, 2012 - 12:30 , Location: Skiles 005 , Jinyong Ma , School of Mathematics, Georgia Tech , Organizer: Christian Houdre
This work studies two topics in sequence analysis. In the first part, we investigate the large deviations of the shape of the random RSK Young diagrams, associated with a random word of size n whose letters are independently drawn from an alphabet of size m=m(n). When the letters are drawn uniformly and when both n and m converge together to infinity, m not growing too fast with respect to n, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. Since the length of the top row of the Young diagrams is the length of the longest (weakly) increasing subsequence of the random word, the corresponding large deviations follow. When the letters are drawn with non-uniform probability, a control of both highest probabilities will ensure that the length of the top row of the diagrams satisfies a large deviation principle. In either case, speeds and rate functions are identified. To complete this first part, non-asymptotic concentration bounds for the length of the top row of the diagrams are obtained. In the second part, we investigate the order of the r-th, 1\le r < +\infty, central moment of the length of the longest common subsequence of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, the r-th central moment is shown to be of order n^{r/2}. In particular, when r=2, the order of the variance is linear.

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