All Seminars & Colloquia

Speaker: Mark Kidwell (U.S. Naval Academy and GWU)

Wednesday, 10/26/2011, 10:06pm - 11:59pm

Abstract: In his book “Low-Dimensional Geometry: From Euclidean Spaces to Hyperbolic Knots”, Francis
Bonahon considers no structure more abstract than a metric space. He then needs to define a metric
on a quotient space, such as the torus obtained by identifying opposite sides of a rectangle. We explore
some quirky consequences of Bonahon’s definition of a (pseudo)-metric on a quotient space. We then
answer the question: does the topology defined by the Bohahon metric on a quotient space coincide
with the quotient topology?

Mochizuki's quandle 3-cocycle invariant of links S^3 is one of the Dijkgraaf-Witten invariants

Speaker: Takefumi Nosaka, RIMS at Kyoto University

Friday, 10/7/2011, 9:11pm - 11:59pm

Abstract: Let p be an odd prime, and \phi the Mochizuki 3-cocycle of "the
dihedral quandle" of order p. Using the 3-cocycle, Carter-Kamada-Saito
combinatorially defined a shadow quandle cocycle invariant of links in
S^3. Let M_L be the double covering branched along a link L. Our main
result is that the cocycle invariant of L equals the Dijkgraaf-Witten
invariant of M_L with respect to the group Z/pZ. We further compute
Dijkgraaf-Witten invariants of some 3-manifolds. In this talk, I

Jointly with Math Colloquium and Applied Math Seminar: Topological Quantum Computation

Zhenghan Wang, Microsoft Research

Thursday, 10/6/2011, 7:45pm - 11:59pm

Modified right-angled Artin groups.

Speaker: Noel Brady, NSF and University of Oklahoma

Tuesday, 9/27/2011, 3:00pm - 11:59pm

Abstract: The family of right-angled Artin groups (RAAGs) interpolates between the family of finitely generated free groups on one hand and the family of finitely generated free abelian groups on the other. RAAGs are easy to define (their definition can be encoded in a finite graph) and have very nice geometric and topological properties (they have non-positively curved cubical classifying spaces). There is a standard map from a RAAG to the integers, and the topological properties of the kernel is reflected in the topology of the clique complex associated to the defining finite graph.

Adiabatic quantum computing: application to NP-hard problems

William de la Cruz, Center of Research and Advanced Studies of IPN, Mexico City

Thursday, 9/22/2011, 5:04pm - 11:59pm

Abstract: Adiabatic quantum computing (AQC) have been shown to be a useful tool for approximating optimization problems. We show an experimental study of the AQC applied to the MaxSat problem.

Homology of Distributive Lattice

Jozef Przytycki, GW

Tuesday, 9/20/2011, 3:14pm - 11:59pm

Abstract: While homology theory of associative structures, such as groups and rings, was extensively studied in the past, beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, has been neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right-) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson.

Adiabatic quantum computing: the construction of Hamiltonian operators

William de la Cruz, Center of Research and Advanced Studies of IPN, Mexico City

Tuesday, 9/13/2011, 5:07pm - 11:59pm

Abstract: Adiabatic Quantum Computing (AQC) has been applied to solve optimization problems. It is based on the construction of Hamiltonian operators which codify the optimal solution of the given optimization problem. AQC makes use of the Adiabatic Theorem to approximate solutions of the Schrödinger equation in which a slow evolution occurs. The Hamiltonian operators used in AQC should be local for convenience. Local Hamiltonian operators are expressed as sums of Hamiltonians operating over a reduced number of qubits.

A connection between odd and even Khovanov homology

Speaker: Krzysztof Putyra (Columbia University)

Monday, 7/25/2011, 8:16pm - 11:59pm