Seminars and Colloquia Schedule

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, April 23, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Will Perkins – Georgia Tech
A discussion of the paper "RNA folding with soft constraints: reconciliation of probing data and thermodynamic secondary structure prediction" by Washietl et al (NAR, 2012).

On a weak form of Arnold diffusion in arbitrary degrees of freedom

Series
CDSNS Colloquium
Time
Monday, April 23, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vadim Kaloshin – Univ. of Maryland
Consider a generic perturbation of a nearly integrable system of {\it arbitrary degrees of freedom $n\ge 2$ system}\[H_0(p)+\eps H_1(\th,p,t),\quad \th\in \T^n,\ p\in B^n,\ t\in \T=\R/\T,\]with strictly convex $H_0$. Jointly with P.Bernard and K.Zhang we prove existence of orbits $(\th,p)(t)$ exhibiting Arnold diffusion \[\|p(t)-p(0) \| >l(H_1)>0 \quad \textup{independently of }\eps.\]Action increment is independent of size of perturbation$\eps$, but does depend on a perturbation $\eps H_1$.This establishes a weak form of Arnold diffusion. The main difficulty in getting rid of $l(H_1)$ is presence of strong double resonances. In this case for $n=2$we prove existence of normally hyperbolic invariant manifolds passing through these double resonances. (joint with P. Bernard and K. Zhang)

Optimization of two-link and three-link snake-like locomotion

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 23, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Fangxu Jing – GT Math
We analyze two-link (or three-link) 2D snake like locomotions and discuss the optimization of the motion. The snake is modeled as two (or three) identical links connected via hinge joints and the relative angles between the links are prescribed as periodic actuation functions. An essential feature of the locomotion is the anisotropy of friction coefficients. The dynamics of the snake is analyzed numerically, as well as analytically for small amplitude actuations of the relative angles. Cost of locomotion is defined as the ratio between distance traveled by the snake and the energy expenditure within one period. Optimal conditions of the highest efficiency in terms of the friction coefficients and the actuations are discussed for the model.

Perturbation Theory and its Application to Complex Biological Networks --A quantification of systematic features of biological networks

Series
Dissertation Defense
Time
Tuesday, April 24, 2012 - 11:00 for 2 hours
Location
Skiles 006
Speaker
Yao Li – School of Mathematics, Georgia Tech
The primary objective of this thesis is to make a quantitative study of complex biological networks. Our fundamental motivation is to obtain the statistical dependency between modules by injecting external noise. To accomplish this, a deep study of stochastic dynamical systems would be essential. The first part is about the stochastic dynamical system theory. The classical estimation of invariant measures of Fokker-Planck equations is improved by the level set method. Further, we develop a discrete Fokker-Planck-type equation to study the discrete stochastic dynamical systems. In the second part, we quantify systematic measures including degeneracy, complexity and robustness. We also provide a series of results on their properties and the connection between them. Then we apply our theory to the JAK-STAT signaling pathway network.

Universality of the global fluctuations for the eigenvectors of Wigner random matrices

Series
Stochastics Seminar
Time
Tuesday, April 24, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
F. Benaych-Georges – Universite Pierre et Marie Curie
Many of the asymptotic spectral characteristics of a symmetric random matrix with i.i.d. entries (such a matrix is called a "Wigner matrix") are said to be "universal": they depend on the exact distribution of the entries only via its first moments (in the same way that the CLT gives the asymptotic fluctuations of the empirical mean of i.i.d. variables as a function of their second moment only). For example, the empirical spectral law of the eigenvalues of a Wigner matrix converges to the semi-circle law if the entries have variance 1, and the extreme eigenvalues converge to -2 and 2 if the entries have a finite fourth moment. This talk will be devoted to a "universality result" for the eigenvectors of such a matrix. We shall prove that the asymptotic global fluctuations of these eigenvectors depend essentially on the moments with orders 1, 2 and 4 of the entries of the Wigner matrix, the third moment having surprisingly no influence.

Overconvergent Lattices and Berkovich Spaces

Series
Algebra Seminar
Time
Tuesday, April 24, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew Dudzik – UC Berkeley
The construction of the Berkovich space associated to a rigid analytic variety can be understood in a general topological framework as a type of local compactification or uniform completion, and more generally in terms of filters on a lattice. I will discuss this viewpoint, as well as connections to Huber's theory of adic spaces, and draw parallels with the usual metric completion of $\mathbb{Q}$.

Mathematics of Crime

Series
School of Mathematics Colloquium
Time
Tuesday, April 24, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Andrea Bertozzi – UCLA Math
There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, methods in linear and nonlinear partial differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes. Examples will consider both "bottom up" and "top down" approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.

Sparse Singular Value Decomposition in High Dimensions

Series
Stochastics Seminar
Time
Tuesday, April 24, 2012 - 16:05 for 1 hour (actually 50 minutes)
Location
skyles 006
Speaker
Zongming Ma – The Wharton School, Department of Statistics, University of Pennsylvania
Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. In this talk, we suppose the true singular vectors have sparse representations in a certain basis. We propose an iterative thresholding algorithm that can estimate the subspaces spanned by leading left and right singular vectors and also the true mean matrix optimally under Gaussian assumption. We further turn the algorithm into a practical methodology that is fast, data-driven and robust to heavy-tailed noises. Simulations and a real data example further show its competitive performance. This is a joint work with Andreas Buja and Dan Yang.

A NEW PARADIGM OF CANCER PROGRESSION AND TREATMENT DISCOVERED THROUGH MATHEMATICAL MODELING: WHAT MEDICAL DOCTORS WON’T TELL YOU

Series
Mathematical Biology Seminar
Time
Wednesday, April 25, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Leonid Khanin – Idaho State University –
Normal 0 false false false EN-US X-NONE X-NONE   Over the last several decades, cancer has become a global pandemic of epic proportions. Unfortunately, treatment strategies resulting from the traditional approach to cancer have met with only limited success. This calls for a paradigm shift in our understanding and treating cancer.    In this talk, we present an entirely mechanistic, comprehensive mathematical model of cancer progression in an individual patient accounting for primary tumor growth, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the age and volume of the primary tumor at diagnosis and volumes of detectable bone metastases collected from one breast cancer and 12 prostate cancer patients. This allowed us to estimate, for each patient, the age at cancer onset and inception of all detected metastasis, the expected metastasis latency time and the rates of growth of the primary tumor and metastases before and after the start of treatment. We found that for all patients: (1) inception of the first metastasis occurred very early when the primary tumor was undetectable; (2) inception of all or most of the surveyed metastases occurred before the start of treatment; (3) the rate of metastasis shedding was essentially constant in time regardless of the size of the primary tumor, and so it was only marginally affected by treatment; and most importantly, (4) surgery, chemotherapy and possibly radiation bring about a dramatic increase in the rate of growth of metastases. Although these findings go against the conventional paradigm of cancer, they confirm several hypotheses that were debated by oncologists for many decades. Some of the phenomena supported by our conclusions, such as the existence of dormant cancer cells and surgery-induced acceleration of metastatic growth, were first observed in clinical investigations and animal experiments more than a century ago and later confirmed in numerous modern studies. 

Some properties of convex hulls of mixed integer points contained in general convex sets.

Series
ACO Student Seminar
Time
Wednesday, April 25, 2012 - 12:00 for 1 hour (actually 50 minutes)
Location
Executive classroom, ISyE Main Building
Speaker
Diego Morán – ISyE, Georgia Tech
A mixed integer point is a vector in $\mathbb{R}^n$ whose first $n_1$ coordinates are integer. We present necessary and sufficient conditions for the convex hull of mixed integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones and strictly convex sets. Furthermore, by using these results, we show that there exists a polynomial time algorithm to check the closedness of the convex hull of the mixed integer points contained in the feasible region of a second order conic programming problem, for the special case this region is defined by just one Lorentz cone and one rational matrix. This is joint work with Santanu Dey.

Bond market models with Levy random factors

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, April 25, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jerzy Zabczyk – Institute of Mathematics, Polish Academy of Sciences

Hosts Christian Houdre and Liang Peng

The talk is devoted to the Heath-Jarrow-Morton modeling of the bond market with stochastic factors of the Levy type. It concentrates on properties of the forward rate process like positivity and mean reversion. The process satisfies a stochastic partial differential equation and sufficient conditions are given under which the equation has a positive global solution. In the special case, when the volatility is a linear functional of the forward curve, the sufficient conditions are close to the necessary ones.

On W. Rudin's problem

Series
Analysis Seminar
Time
Wednesday, April 25, 2012 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Konstantin Oskolkov – University of South Carolina

Regularity of solutions to degenerate p-Laplace equations

Series
Analysis Seminar
Time
Wednesday, April 25, 2012 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kabe Moen – University of Alabama
Motivated by mappings of finite distortion, we consider degenerate p-Laplacian equations whose ellipticity condition is satisfied by thedistortion tensor and the inner distortion function of such a mapping. Assuming a certain Muckenhoupt type condition on the weightinvolved in the ellipticity condition, we describe the set of continuity of solutions.

A new bound for the 2/3 Conjecture

Series
Graph Theory Seminar
Time
Thursday, April 26, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Whalen – Math, GT
We show that any n-vertex complete graph with edges colored with three colors contains a set of at most four vertices such that the number of the neighbors of these vertices in one of the colors is at least 2n/3. The previous best value proved by Erdos et al in 1989 is 22. It is conjectured that three vertices suffice. This is joint work with Daniel Kral, Chun-Hung Liu, Jean-Sebastien Sereni, and Zelealem Yilma.

Graduate Student Probability Conference

Series
Other Talks
Time
Friday, April 27, 2012 - 08:30 for 8 hours (full day)
Location
Klaus 1116
Speaker
Probability Graduate Students – School of Mathematics, Georgia Tech
Georgia Tech School of Mathematics will host the 6th Annual Graduate Student Probability Conference (GSPC) from April 27-29, 2012. The conference is open to all graduate students and post-doctoral fellows interested in probability. The two keynote speakers this year are: Professor Jean Bertoin, Universität Zürich; Professor Craig Tracy, University of California

5-List-Coloring Graphs on Surfaces

Series
ACO Student Seminar
Time
Friday, April 27, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Executive classroom, ISyE Main Building
Speaker
Luke Postle – School of Math., Georgia Tech
Thomassen proved that there are only finitely many 6-critical graphs embeddable on a fixed surface. He also showed that planar graphs are 5-list-colorable. We develop new techniques to prove a general theorem for 5-list-coloring graphs embedded on a fixed surface. Namely, for every surface S and every integer C > 0, there exists D such that the following holds: Let G be a graph embedded in a surface S with edge-width at least D and a list assignment L such that, for every vertex v in G, L(v) has size at least five. If F is a collection of any number of facial cycles of length at most C such that every two cycles in F are distance at least D apart and every cycle in F has a locally planar neighborhood up to distance D/2, then any proper L-coloring of F extends to an L-coloring of G. This theorem implies the following results. In what follows, let S be a fixed surface, G be a graph embedded in S (except in 4, where G is drawn in S) and L a list assignment such that, for every vertex v of G, L(v) has size at least five. 1. If G has large edge-width, then G is 5-list-colorable. (Devos, Kawarabayashi and Mohar) 2. There exists only finitely many 6-list-critical graphs embeddable in S. (Conjectured by Thomassen, Proof announced by Kawarabayashi and Mohar) As a corollary, there exists a linear-time algorithm for deciding 5-list-colorability of graphs embeddable on S. Furthermore, we exhibit an explicit bound on the size of such graphs. 3. There exists D(S) such that the following holds: If X is a subset of the vertices of G that are pairwise distance at least D(S) apart, then any L-coloring of X extends to an L-coloring G. For planar graphs, this was conjectured by Albertson and recently proved by Dvorak, Lidicky, Mohar, and Postle. 4. There exists D(S) such that the following holds: If G is a graph drawn in S with face-width at least D(S) such that any pair of crossings is distance at least D apart, then G is L-colorable. For planar graphs, this was recently proved by Dvorak, Lidicky and Mohar. Joint work with Robin Thomas.

Towards Sarkozy's Problem

Series
Combinatorics Seminar
Time
Friday, April 27, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ernie Croot – School of Math, Ga Tech –
Sarkozy's problem is a classical problem in additive number theory, which asks for the size of the largest subset A of {1,2,...,n} such that the difference set A-A does not contain a (non-zero) square. I will discuss the history of this problem, some recent progress that I and several collaborators have made on it, and our future research plans.

Southeast Geometry Seminar

Series
Other Talks
Time
Sunday, April 29, 2012 - 08:30 for 8 hours (full day)
Location
Skiles 005
Speaker
Southeast Geometry Seminar – School of Mathematics, Georgia Tech

The general public lecture will be presented by Jason Cantarella (University of Georgia) entitled<br />
The Square Peg Theorems or What does it mean to solve simultaneous equations? to take place in Klaus 1116 at 5:00PM

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. Jason Cantarella (University of Georgia);   Meredith Casey (The Georga Institute of Technology);  Kirk Lancaster (Wichita State University); Junfang Li ( University of Alabama at Birmingham)  Jason Parsley (Wake Forest University);