Date 
Speaker 
Affiliation 
Title 
Abstract 
Apr 11 (MONDAY, 3:00pm in CB3 1.314) 
Hitoshi Murakami 
Tohoku University, Japan 
An introduction to the volume conjecture, I 
We define the Jones polynomial and show it is an invariant for knots in the threedimensional space. Then we define the "colored" Jones polynomial. 
Apr 12 (TUESDAY, 11am in JSOM 11.206) 
Hitoshi Murakami 
Tohoku University, Japan 
An introduction to the volume conjecture, II 
We quickly introduce the threedimensional hyperbolic geometry. We also show that the complement of the figureeight knot has a hyperbolic structure.

Apr 13 (WEDNESDAY, 2:30pm in CB3 1.314) 
Hitoshi Murakami 
Tohoku University, Japan 
An introduction to the volume conjecture, III 
We introduce the volume conjecture and prove it in the case of the figureeight knot. Indeed, we show that a certain limit of the colored Jones polynomial defines the volume of the complement of the figureeight knot.

Feb 29 (MONDAY, 2:30pm in FN 2.202) 
Takayuki Morifuji 
Keio University, Japan 
Twisted Alexander polynomial and its applications I 
In this series of 3 onehour lectures, we explain basic properties of twisted Alexander
polynomials and discuss some applications to topology of 3dimensional
manifolds (in particular of knot complements in the 3sphere). More precisely,
we focus on fibering and genus detecting problems, and further we mention
a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots. 
Mar 1 (TUESDAY, 11am in JSOM 11.206) 
Takayuki Morifuji 
Keio University, Japan 
Twisted Alexander polynomial and its applications II 

Mar 2 (WEDNESDAY, 2:30pm in FN 2.202) 
Takayuki Morifuji 
Keio University, Japan 
Twisted Alexander polynomial and its applications III 






Nov 2 
Cesare Tronci 
University of Surrey, UK 
Variational and Poissonbracket approaches to quantum dynamics 
Starting from the DiracFrenkel Lagrangian for pure quantum states, symmetry methods are applied to provide new variational principles for the dynamics of pure and mixed states in different pictures (Schrödinger, Heisenberg, Dirac, WignerMoyal, and Ehrenfest). In addition, a hybrid classicalquantum Poisson bracket is provided for expectation value dynamics, which is then shown to be canonical (Hamiltonian) for any quantum state. 
Oct 12 
Razvan Gelca 
Texas Tech University 
ChernSimons theory and Weyl quantization 
ChernSimons theory is a quantum theory based on the ChernSimons Lagrangian, and was introduced by E. Witten to explain the Jones polynomial of knots. Since its introduction, this theory proved to have a unifying nature, bringing together quantum theory, 3dimensional topology and geometry, representation theory, and algebraic geometry. This talk is based on a discovery made by the speaker in joint work with Alejandro Uribe, which shows that the quantization model introduced by H. Weyl in 1931 plays a central role in ChernSimons theory. 
Oct 5 
Cynthia Curtis 
College of New Jersey 
The SL(2,C) Casson invariant for knots and the Apolynomial 
Lowdimensional topologists study both knots and 3dimensional manifolds, and in fact all 3dimensional manifolds can be constructed using knots. We explain this relationship and discuss how we can study both knots and 3manifolds by looking at representations of groups associated to the knots and 3manifolds. We focus on two invariants of knots and 3manifolds which are constructed from such representations, the SL(2, C) Casson invariant and the Apolynomial. We show that the SL(2, C) Casson invariant predicts the degrees of a variant of the Apolynomial and discuss the computability and power of each. 
Sep 28 
Maxim Arnold 
UT Dallas 
On the shock function for planar Burgers equation (cont'd) 
It is wellknown that zeroviscosity Burgers equation posses a finitetime singularity. Such a singularity is often called a shock. To construct a solution after shock formation one needs to define a velocity vector field in the point of the shock. This can be done using various methods. I will describe a geometric construction for this and use it to describe the set of points falling to the shock. 
Sep 21 
Maxim Arnold 
UT Dallas 
On the shock function for planar Burgers equation 
It is wellknown that zeroviscosity Burgers equation posses a finitetime singularity. Such a singularity is often called a shock. To construct a solution after shock formation one needs to define a velocity vector field in the point of the shock. This can be done using various methods. I will describe a geometric construction for this and use it to describe the set of points falling to the shock. 
Sep 14 
Susan Aberanathy 
Angelo State University 
Genus1 tangles and Kauffman bracket ideals 
A genus1 tangle is a 1manifold with two boundary components properly embedded in the solid torus. A genus1 tangle G embeds in a link L if G can be completed to L by a 1manifold in the complement of the solid torus containing G. A natural question to ask is: given a tangle G and a link L, how can we tell if G embeds in L? We discuss the Kauffman bracket ideal (along with its even and odd versions) which gives an obstruction to embedding, and outline a method for computing a finite list of generators for these ideals. We also examine some specific examples and use our method to compute their Kauffman bracket ideals. 