Seminars and Colloquia by Series

Obtaining Protein Energetics Using Adaptive Steered Molecular Dynamics

Series
Mathematical Biology Seminar
Time
Wednesday, February 19, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rigoberto Hernandez – GT Chem & Biochem
The behavior and function of proteins necessarily occurs during nonequilibrium conditions such as when a protein unfolds or binds. The need to treat both the dynamics and the high-dimensionality of proteins and their environments presents significant challenges to theoretical or computational methods. The present work attempts to reign in this complexity by way of capturing the dominant energetic pathway in a particular protein motion. In particular, the energetics of an unfolding event can be formally obtained using steered molecular dynamics (SMD) and Jarzynski’s inequality but the cost of the calculation increases dramatically with the length of the pathway. An adaptive algorithm has been introduced that allows for this pathway to be nonlinear and staged while reducing the computational cost. The potential of mean force (PMF) obtained for neuropeptide Y (NPY) in water along an unfolding path confirmed that the monomeric form of NPY adopts the pancreatic-polypeptide (PP) fold. [J. Chem. Theory Comput. 6, 3026-3038 (2010); 10.1021/ct100320g.] Adaptive SMD can also be used to reconstruct the PMF obtained earlier for stretching decaalanine in vacuum at lower computational cost. [J. Chem. Phys. 136, 215104 (2012); 10.1063/1.4725183.] The PMF for stretching decaalanine in water solvent (using the TIP3P water potential) at 300K has now been obtained using adaptive SMD. [J. Chem. Theory Comput. 8, 4837 (2012); 10.1021/ct300709u] Not surprisingly, the stabilization from the water solvent reduces the overall work required to unfold it. However, the PMF remains structured suggesting that some regions of the energy landscape act partially as doorways. This is also further verified through a study of the hydrogen-bond breaking and formation along the stretching paths of decaalanine in vacuum and solvent. (Rescheduled from Feb 12th.)

Some New Comparison Results in Balls and Shells

Series
PDE Seminar
Time
Tuesday, February 18, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeffrey Langford – Bucknell University
In a comparison theorem, one compares the solution of a given PDE to a solution of a second PDE where the data are "rearranged." In this talk, we begin by discussing some of the classical comparison results, starting with Talenti's Theorem. We then discuss Neumann comparison results, including a conjecture of Kawohl, and end with some new results in balls and shells involving cap symmetrization.

Tropical Laplacians and the Colin de Verdiere number of graphs

Series
Algebra Seminar
Time
Monday, February 17, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric Katz – University of Waterloo
Given a surface in space with a set of curves on it, one can ask whichpossible combinatorial arrangement of curves are possible. We give anenriched formulation of this question in terms of which two-dimensionalfans occur as the tropicalization of an algebraic surface in space. Ourmain result is that the arrangement is either degenerate or verycomplicated. Along the way, we introduce tropical Laplacians, ageneralization of graph Laplacians, explain their relation to the Colin deVerdiere invariant and to tensegrity frameworks in dynamics.This is joint work with June Huh.

Hamiltonian Circle Actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds

Series
Geometry Topology Seminar
Time
Monday, February 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew Fanoe – Morehouse College
The question of what conditions guarantee that a symplectic$S^1$ action is Hamiltonian has been studied for many years. Sue Tolmanand Jonathon Weitsman proved that if the action is semifree and has anon-empty set of isolated fixed points then the action is Hamiltonian.Furthermore, Cho, Hwang, and Suh proved in the 6-dimensional case that ifwe have $b_2^+=1$ at a reduced space at a regular level $\lambda$ of thecircle valued moment map, then the action is Hamiltonian. In this paper, wewill use this to prove that certain 6-dimensional symplectic actions whichare not semifree and have a non-empty set of isolated fixed points areHamiltonian. In this case, the reduced spaces are 4-dimensional symplecticorbifolds, and we will resolve the orbifold singularities and useJ-holomorphic curve techniques on the resolutions.

Scattering Resonances for Photonic Structures and Schrodinger Operators

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Junshan Lin – Auburn University
Resonances are important in the study of transient phenomenaassociated with the wave equation, especially in understanding the largetime behavior of the solution to the wave equation when radiation lossesare small. In this talk, I will present recent studies on the scatteringresonances for photonic structures and Schrodinger operators. I will beginwith a study on the finite symmetric photoinc structure to illustrate theconvergence behavior of resonances. Then a general perturbation approachwill be introduced for the analysis of near bound-state resonances for bothcases. In particular, it is shown that, for a finite one dimensionalphotonic crystal with a defect, the near bound-state resonances converge tothe point spectrum of the infinite structure with an exponential rate whenthe number of periods increases. An analogous exponential decay rate alsoholds for the Schrodinger operator with a potential function that is alow-energy well surrounded by a thick barrier. The analysis also leads to asimple and accurate numerical approach to approximate the near bound-stateresonances. This is a joint work with Prof. Fadil Santosa in University ofMinnesota.

Finite Cyclicity of HH-graphics with a Triple Nilpotent Singularity of Codimension 3 or 4

Series
CDSNS Colloquium
Time
Monday, February 17, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chunhua Shan – School of Mathematics, Georgia Institute of Technology
In 1994, Dumortier, Roussarie and Rousseau launched a program aiming at proving the finiteness part of Hilbert’s 16th problem for the quadratic system. For the program, 121 graphics need to be proved to have finite cyclicity. In this presentation, I will show that 4 families of HH-graphics with a triple nilpotent singularity of saddle or elliptic type have finite cyclicity. Finishing the proof of the cyclicity of these 4 families of HH-graphics represents one important step towards the proof of the finiteness part of Hilbert’s 16th problem for quadratic systems. This is a joint work with Professor Christiane Rousseau and Professor Huaiping Zhu.

The Logarithmic Integral

Series
Analysis Working Seminar
Time
Friday, February 14, 2014 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Kelly Bickel – School of Math
Kelly will be leading the discussion and presenting topics from Chapter 2 Section 4 of Bounded Analytic Functions.

A topological approach to investigating the structure of neural activity

Series
Job Candidate Talk
Time
Thursday, February 13, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vladimir Itskov – U. of Nebraska
Experimental neuroscience is achieving rapid progress in the ability to collect neural activity and connectivity data. This holds promise to directly test many theoretical ideas, and thus advance our understanding of "how the brain works." How to interpret this data, and what exactly it can tell us about the structure of neural circuits, is still not well-understood. A major obstacle is that these data often measure quantities that are related to more "fundamental" variables by an unknown nonlinear transformation. We find that combinatorial topology can be used to obtain meaningful answers to questions about the structure of neural activity. In this talk I will first introduce a new method, using tools from computational topology, for detecting structure in correlation matrices that is obscured by an unknown nonlinear transformation. I will illustrate its use by testing the "coding space" hypothesis on neural data. In the second part of my talk I will attempt to answer a simple question: given a complete set of binary response patterns of a network, can we rule out that the network functions as a collection of disconnected discriminators (perceptrons)? Mathematically this translates into questions about the combinatorics of hyperplane arrangements and convex sets.

The Sherrington-Kirkpatrick model and its diluted version (**Cancelled due to inclement weather**)

Series
School of Mathematics Colloquium
Time
Thursday, February 13, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dmitry Panchenko – Texas A&M University
Abstract: I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main goals in these models is to find a formula for the maximum of the process, or the free energy, in the limit when the size of the system is getting large. The answer depends on understanding the structure of the Gibbs measure in a certain sense, and this structure is expected to be described by the so called Parisi solution in the SK model and Mézard-Parisi solution in the diluted SK model. I will explain what these are and mention some results in this direction.

Overview of Yamabe problem

Series
Geometry Topology Student Seminar
Time
Wednesday, February 12, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech.
We will give an overview of ideas that go into solution of Yamabe problem: Given a compact Riemannian manifold (M,g) of dimension n > 2, find a metric conformal to g with constant scalar curvature.

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