Seminars and Colloquia by Series

Markov Perfect Nash Equilibria: some considerations on Economic Models, Dynamical Systems and Statistical Mechanics.

Series
Research Horizons Seminar
Time
Wednesday, November 3, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Federico BonettoSchool of Mathematics - Georgia Institute of Technology

Please Note: Hosts: Yao Li and Ricardo Restrepo

Modern Economic Theory is largely based on the concept of Nash Equilibrium. In its simplest form this is an essentially statics notion. I'll introduce a simple model for the origin of money (Kiotaki and Wright, JPE 1989) and use it to introduce a more general (dynamic) concept of Nash Equilibrium and my understanding of its relation to Dynamical Systems Theory and Statistical Mechanics.

On an analogue of Torelli's theorem for tropical curves

Series
Tropical Geometry Seminar
Time
Wednesday, November 3, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Farbod ShokriehGeorgia Tech
In classical algebraic geometry,Torelli's theorem states that a complete smooth curve over an algebraically closed field is uniquely determined by its principally polarized Jacobian. We will investigate a tropical analogue of this theorem. Torelli's problem for tropical curves is intimately related to some basic combinatorial questions regarding the cycle space of a finite graph. Combinatorics of the Voronoi (or Delaunay) decomposition associated to the cycle lattice play an essential role. This talk will be self-contained. The talk next week (by Melody Chan) can be considered a natural sequel.

Persistence of a single phytoplankton species

Series
PDE Seminar
Time
Tuesday, November 2, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Yuan LouOhio State University
We investigate a nonlocal reaction-diffusion-advection equation which models the growth of a single phytoplankton species in a water column where the species depends solely on light for its metabolism. We study the combined effect of death rate, sinking or buoyant coe±cient, water column depth and vertical turbulent diffusion rate on the persistence of a single phytoplankton species. This is based upon a joint work with Sze-Bi Hsu, National Tsing-Hua University.

Decimations of l-sequences and permutations of even residues mod p

Series
Combinatorics Seminar
Time
Friday, October 29, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Todd CochraneMath, Kansas State University
\ell-sequences are periodic binary sequences {a_i} that arise from Feedback with Carry Shift Registers and in many other ways. A decimation of {a_i} is a sequence of the form {a_{di}}. Goresky and Klapper conjectured that for any prime p>13 and any \ell-sequence based on p, every pair of allowable decimations of {a_i} is cyclically distinct. If true this would yield large families of binary sequences with ideal arithmetic cross correlations. The conjecture is essentially equivalent to the statement that if p>13 then the mapping x \to Ax^d on \mathbb Z/(p) with (d,p-1)=1, p \nmid A, permutes the even residues only if it is the identity mapping. We will report on the progress towards resolving this conjecture, focussing on our joint work with Bourgain, Paulhus and Pinner.

Non-commutative Geometry III: Crossed Product and Orbit Space of Group Actions

Series
Geometry Topology Working Seminar
Time
Friday, October 29, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean BellissardGa Tech

Please Note: Note this is a 2 hour talk.

An action of the real line on a compact manifold defines a topological dynamical system. The set of orbits might be very singular for the quotient topology. It will be shown that there is, however, a C*-algebra, called the crossed product, which encodes the topology of the orbit space. The construction of this algebra can be done for an group action, if the group is locally compact.

When do random CSPs become hard?

Series
SIAM Student Seminar
Time
Friday, October 29, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ricardo RestrepoSchool of Mathematics, Georgia Tech
A constraint satisfaction problem (CSP) is an ensemble of boolean clauses, where satisfaction is obtained by an assignment of the variables if every clause is satisfied by such assignment. We will see that when such CSP is arranged following certain random structure, the Fourier expansion of the corresponding clauses allows us to understand certain properties of the solution space, in particular getting a partial understanding of when the 'usual suspects' of the drastical failure of all known satisfiability algorithms, namely long range correlations and clustering, appear. Based in joint work with Prasad Tetali and Andrea Montanari.

Displaying blocking pairs in signed graphs

Series
ACO Seminar
Time
Thursday, October 28, 2010 - 16:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Bertrand GueninDept. of Combinatorics and Optimization, University of Waterloo
A signed graph is a pair (G, \Sigma) where G is a graph and \Sigma is a subset of the edges of G. A cycle C in G is even (resp. odd) if E(C) \cap \Sigma is even (resp. odd). A blocking pair in a signed graph is a pair of vertices {x, y} such that every odd cycle in (G, \Sigma) intersects at least one of the vertices x and y. Blocking pairs arise in a natural way in the study of even cycle matroids on signed graphs as well as signed graphs with no odd K_5 minor. In this article, we characterize when the blocking pairs of a signed graph can be represented by 2-cuts in an auxiliary graph. We discuss the relevance of this result to the problem of characterizing signed graphs with no odd K_5 minor and determing when two signed graphs represent the same even cycle matroid. This is joint work with Irene Pivotto and Paul Wollan.

Balanced Vertices in Trees and a Simpler Algorithm to Compute the Genomic Distance

Series
Combinatorics Seminar
Time
Thursday, October 28, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Peter L.ErdosAlfred Renyi Inst. of Mathematics, Budapest
In this talk we will report a short and transparent solution for the covering cost of white--grey trees which play a crucial role in the algorithm of Bergeron et al. to compute the rearrangement distance between two multi-chromosomal genomes in linear time (Theor. Comput. Sci., 410:5300-5316, 2009). In the process it introduces a new center notion for trees, which seems to be interesting on its own.

Euler's pentagonal numbers theorem - refinements, variations and companions

Series
School of Mathematics Colloquium
Time
Thursday, October 28, 2010 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 249
Speaker
Krishnaswami AlladiUniversity of Florida
Euler's celebrated pentagonal numbers theorem is one themost fundamental in the theory of partitions and q-hypergeometric series.The recurrence formula that it yields is what MacMahon used to compute atable of values of the partition function to verify the deep Hardy-Ramanujanformula. On seeing this table, Ramanujan wrote down his spectacular partition congruences. The author recently proved two new companions to Euler'stheorem in which the role of the pentagonal numbers is replaced by the squares.These companions are deeper in the sense that lacunarity can be achievedeven with the introduction of a parameter. One of these companions isdeduced from a partial theta identity in Ramanujan's Lost Notebook and theother from a q-hypergeometric identity of George Andrews. We will explainconnections between our companions and various classical results such asthe Jacobi triple product identity for theta functions and the partitiontheorems of Sylvester and Fine. The talk will be accessible to non-experts.

Rational Inner Functions in the Schur-Agler Class

Series
Analysis Seminar
Time
Wednesday, October 27, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Greg KneseUniversity of Alabama
The Schur-Agler class is a subclass of the bounded analytic functions on the polydisk with close ties to operator theory. We shall describe our recent investigations into the properties of rational inner functions in this class. Non-minimality of transfer function realization, necessary and sufficient conditions for membership (in special cases), and low degree examples are among the topics we will discuss.

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