Seminars and Colloquia by Series

Genericity of chaotic behavior

Series
School of Mathematics Colloquium
Time
Thursday, September 27, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yakov Pesin – Penn State
It is well-known that a deterministic dynamical system can exhibit stochastic behavior that is due to the fact that instability along typical trajectories of the system drives orbits apart, while compactness of the phase space forces them back together. The consequent unending dispersal and return of nearby trajectories is one of the hallmarks of chaos. The hyperbolic theory of dynamical systems provides a mathematical foundation for the paradigm that is widely known as "deterministic chaos" -- the appearance of irregular chaotic motions in purely deterministic dynamical systems. This phenomenon is considered as one of the most fundamental discoveries in the theory of dynamical systems in the second part of the last century. The hyperbolic behavior can be interpreted in various ways and the weakest one is associated with dynamical systems with non-zero Lyapunov exponents. I will discuss the still-open problem of whether dynamical systems with non-zero Lyapunov exponents are typical. I will outline some recent results in this direction. The genericity problem is closely related to two other important problems in dynamics on whether systems with nonzero Lyapunov exponents exist on any phase space and whether nonzero exponents can coexist with zero exponents in a robust way.

Ends of Nonpositively Curved Manifolds

Series
Research Horizons Seminar
Time
Wednesday, September 26, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Igor Belegradek – Georgia Tech, School of Math
In the talk we will start from examples of open surfaces, such as the complex plane minus a Cantor set, review their classification, and then move to higher dimensions, where we discuss ends of manifolds in the topological setting, and finally in the geometric setting under the assumption of nonpositive curvature.

On the extension of sharp Hardy-Littlewood-Sobolev inequality

Series
PDE Seminar
Time
Tuesday, September 25, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Meijun Zhu – University of Oklahoma
We shall describe our recent work on the extension of sharp Hardy-Littlewood-Sobolev inequality, including the reversed HLS inequality with negative exponents. The background and motivation will be given. The related integral curvature equations may be discussed if time permits.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Tuesday, September 25, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Will Perkins – Georgia Tech
Further discussion of co-transcriptional RNA folding, and the potential for trap models to capture these dynamics.

Algorithms for symmetric Gröbner bases

Series
Algebra Seminar
Time
Monday, September 24, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Krone – Georgia Tech
A symmetric ideal in the polynomial ring of a countable number of variables is an ideal that is invariant under any permutations of the variables. While such ideals are usually not finitely generated, Aschenbrenner and Hillar proved that such ideals are finitely generated if you are allowed to apply permutations to the generators, and in fact there is a notion of a Gröbner bases of these ideals. Brouwer and Draisma showed an algorithm for computing these Gröbner bases. Anton Leykin, Chris Hillar and I have implemented this algorithm in Macaulay2. Using these tools we are exploring the possible invariants of symmetric ideals that can be computed, and looking into possible applications of these algorithms, such as in graph theory.

Towards flexibility for higher-dimensional contact manifolds

Series
Geometry Topology Seminar
Time
Monday, September 24, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Olga Plamenevskaya – SUNY - Stony Brook
By a classical result of Eliashberg, contact manifolds in dimension 3 come in two flavors: tight (rigid) and overtwisted (flexible). Characterized by the presence of an "overtwisted disk", the overtwisted contact structures form a class where isotopy and homotopy classifications are equivalent.In higher dimensions, a class of flexible contact structures is yet to be found. However, some attempts to generalize the notion of an overtwisted disk have been made. One such object is a "plastikstufe" introduced by Niederkruger following some ideas of Gromov. We show that under certain conditions, non-isotopic contact structures become isotopic after connect-summing with a contact sphere containing a plastikstufe. This is a small step towards finding flexibility in higher dimensions. (Joint with E. Murphy, K. Niederkruger, and A. Stipsicz.)

Modeling transcriptional elongation

Series
CDSNS Colloquium
Time
Monday, September 24, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tomas Gedeon – Montana State University –

Please Note: Joint with Applied and Computational Mathematics Seminar

Bio-polymerization processes like transcription and translation are central to a proper function of a cell. The speed at which the bio-polymer grows is affected both by number of pauses of elongation machinery, as well their numbers due to crowding effects. In order to quantify these effects in fast transcribing ribosome genes, we rigorously show that a classical traffic flow model is a limit of mean occupancy ODE model. We compare the simulation of this model to a stochastic model and evaluate the combined effect of the polymerase density and the existence of pauses on transcription rate of ribosomal genes.

Minimum linear ordering problems under submodular costs

Series
Combinatorics Seminar
Time
Friday, September 21, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prasad Tetali – Georgia Tech –
We introduce a general Minimum Linear Ordering Problem (MLOP): Given a nonnegative set function f on a finite set V, find a linear ordering on V such that the sum of the function values for all the suffixes is minimized. This problem generalizes well-known problems such as the Minimum Linear Arrangement, Min Sum Set Cover, and Multiple Intents Ranking. Extending a result of Feige, Lovasz, and Tetali (2004) on Min Sum Set Cover, we show that the greedy algorithm provides a factor 4 approximate optimal solution when the cost function f is supermodular. We also present a factor 2 rounding algorithm for MLOP with a monotone submodular cost function, while the non monotone case remains wide open. This is joint work with Satoru Iwata and Pushkar Tripathi.

Unfoldings of affine convex polytopes

Series
Geometry Topology Working Seminar
Time
Friday, September 21, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mohammad Ghomi – Georgia Tech –
A well-known problem in discerte convex geometry, attributed to the Dutch painter Durrer and first formulated by G. C. Shephard, is concerned with whether every convex polyope P in Euclidean 3-space has a simpe net, i.e., whether the surface of P can be isometrically embedded in the Euclidean plane after it has been cut along some spanning tree of its edges. In this talk we show that the answer is yes after an affine transformation. In particular the combinatorial structure of P plays no role in deciding its unfoldability, which settles a question of Croft, Falconer, and Guy. The proof employs a topological lemma which provides a criterion for checking embeddedness of immersed disks.

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