# All Seminars & Colloquia

Character Varieties of surfaces as completely integrable systems

Adam Sikoa, University at Buffalo.

Tuesday, 11/22/2011, 4:10pm - 11:59pm

**Abstract**: It is known that the trace functions of a maximal set of disjoint simple closed curves on a closed surface make its SU(2)-character variety into an (almost) completely integrable dynamical system. We prove an analogous statement for all rank 2 Lie groups. We will discuss the possible generalizations of this result to higher ranks and,

if time permits, its applications to quantization of character varieties.

Adiabatic quantum computing: equivalence with quantum computing

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

Thursday, 11/3/2011, 5:00pm - 11:59pm

Abstract: The adiabatic quantum computing (AQC) was originally introduced to solve optimization problems by constructing two Hamiltonian operators where the first one is easy to prepare and the second one codifies the solution of the considered problem. Van Dam et al. (2001) proved that AQC performs universal computing by showing that the adiabatic evolution can be simulated with quantum circuits of polynomial size. In this talk we review van Dam's construction in order to understand the complexity of AQC and its limitations

The Bonahon Metric and Topology

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