Seminars and Colloquia by Series

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.

Groebner Bases and Integer Programming

Series
ACO Student Seminar
Time
Friday, September 21, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josephine Yu – Georgia Tech
The theory of Groebner bases is the foundation of many algorithms in computational algebra. A Groebner basis is a special generating set of an ideal of polynomials. In this expository talk, I will introduce Groebner bases and explain how they can be used in integer programming. In particular, for an integer program, we can associate an ideal whose Groebner basis gives a set of directions that takes any feasible solution to an optimal solution.

Estimation and Support Recovery with Exponential Weights

Series
Stochastics Seminar
Time
Thursday, September 20, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Karim Lounici – Georgia Institute of Technology –
In the context of a linear model with a sparse coefficient vector, sharp oracle inequalities have been established for the exponential weights concerning the prediction problem. We show that such methods also succeed at variable selection and estimation under near minimum condition on the design matrix, instead of much stronger assumptions required by other methods such as the Lasso or the Dantzig Selector. The same analysis yields consistency results for Bayesian methods and BIC-type variable selection under similar conditions. Joint work with Ery Arias-Castro

Stochastic volatility with long-memory in discrete and continuous time

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, September 19, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Frederi Viens – Purdue University

Please Note: Hosts Christian Houdre and Liang Peng

It is commonly accepted that certain financial data exhibit long-range dependence. A continuous time stochastic volatility model is considered in which the stock price is geometric Brownian motion with volatility described by a fractional Ornstein-Uhlenbeck process. Two discrete time models are also studied: a discretization of the continuous model via an Euler scheme and a discrete model in which the returns are a zero mean iid sequence where the volatility is a fractional ARIMA process. A particle filtering algorithm is implemented to estimate the empirical distribution of the unobserved volatility, which we then use in the construction of a multinomial recombining tree for option pricing. We also discuss appropriate parameter estimation techniques for each model. For the long-memory parameter, we compute an implied value by calibrating the model with real data. We compare the performance of the three models using simulated data and we price options on the S&P 500 index. This is joint work with Prof. Alexandra Chronopoulou, which appeared in Quantitative Finance, vol 12, 2012.

The onset of turbulence in pipe flow

Series
Math Physics Seminar
Time
Wednesday, September 19, 2012 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Dwight Barkley – Mathematics Institute, University of Warwick

Please Note: Host: Predrag Cvitanovic

More than 125 years ago Osborne Reynolds launched the quantitative study of turbulent transition as he sought to understand the conditions under which fluid flowing through a pipe would be laminar or turbulent. Since laminar and turbulent flow have vastly different drag laws, this question is as important now as it was in Reynolds' day. Reynolds understood how one should define "the real critical value'' for the fluid velocity beyond which turbulence can persist indefinitely. He also appreciated the difficulty in obtaining this value. For years this critical Reynolds number, as we now call it, has been the subject of study, controversy, and uncertainty. Now, more than a century after Reynolds pioneering work, we know that the onset of turbulence in shear flows is properly understood as a statistical phase transition. How turbulence first develops in these flows is more closely related to the onset of an infectious disease than to, for example, the onset of oscillation in the flow past a body or the onset of motion in a fluid layer heated from below. Through the statistical analysis of large samples of individual decay and proliferation events, we at last have an accurate estimate of the real critical Reynolds number for the onset of turbulence in pipe flow, and with it, an understanding of the nature of transitional turbulence. This work is joint with: K. Avila, D. Moxey, M. Avila, A. de Lozar, and B. Hof.

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