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Spring Semester 2017
Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.
Date / Time  Speaker  Title  Location  

23 February 2017 15:1516:15 
Wellington Galleas ETH Zurich 
Partition function of the elliptic gl_{2} SoS model as a single determinant  HG G 43  
Abstract: Partition functions of vertex models with domainwall boundaries have appeared in a variety of contexts ranging from enumerative combinatorics to the study of gauge theories. The sixvertex model is the prototype model where such boundary conditions were adopted and, in that case, the model's partition function admits a compact representation in terms of a single determinant. Such representation has led to a number of developments in the field but seemed to be restricted to the sixvertex model. The next natural candidate for this study is the elliptic gl_{2} SolidonSolid (SoS) model but, despite all efforts, the results suggested single determinantal representations did not exist. This problem has only been recently solved with the help of special functional equations originating from the dynamical version of the YangBaxter algebra. In this talk I will discuss this problem and show how families of single determinantal representations for the elliptic SoS model's partition function can be derived in a constructive manner.  
2 March 2017 15:1516:15 
Alexander Veselov Loughborough University 
Lyapunov spectrum for Markov dynamics and hyperbolic structures  HG G 43  
Abstract: We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x ∈ RP^{1} on a binary planar tree, describing the growth of Markov triples and their ``tropical" version  Euclid triples. We show that the corresponding Lyapunov spectrum is [0, ln φ], where φ is the golden ratio, and prove that on the set X of the most irrational numbers the corresponding function Λ_{X} is convex and strictly monotonic. The key step is using the relation of Markov numbers with hyperbolic structures on punctured torus, going back to D. Gorshkov and H. Cohn, and, more precisely, the recent result by V. Fock, who combined this with Thurston’s lamination ideas. The talk is based on joint work with K. Spalding.  
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9 March 2017 14:1515:15 
Ping Xu Penn State University 
Formality theorem and KontsevichDuflo theorem for Lie pairs  HG G 19.1  
Abstract: A Lie pair (L,A) consists of a Lie algebra (or more generally, a Lie algebroid) L together with a Lie subalgebra (or Lie subalgebroid) A. A wide range of geometric situations can be described in terms of Lie pairs including complex manifolds, foliations, and manifolds equipped with Lie group actions. To each Lie pair (L,A) are associated two Linfinity algebras, which play roles similar to the spaces of polyvector fields and polydifferential operators. We establish the formality theorem for Lie pairs. As an application, we obtain KontsevichDuflo type theorem for Lie pairs. Besides using Kontsevich formality theorem, our approach is based on the construction of a dg manifold (L[1] + L/A, Q) together with a dg foliation, called the Fedosov dg Lie algebroid. This is a joint work with HsuanYi Liao and Mathieu Stienon.  
16 March 2017 15:1516:15 
Ben Kohli Université de Bourgogne 
The LinksGould invariants seen as generalizations of the Alexander polynomial  HG G 43  
Abstract: The LinksGould invariants are a family of two variable quantum link isotopy invariants. They are derived from Hopf superalgebras U_q(gl(mn)). However we now know that the Alexander invariant can be obtained through several different evaluations from the LinksGould polynomial,using work by De WitIshiiLinks, and more recently joint work with Bertrand PatureauMirand. Therefore all the information contained in the Alexander polynomial can be found inside the LinksGould invariants, including the homological information: lower bound for the genus, criterion for fiberedness of knots, ... So we can wonder whether the LinksGould invariants generalize any classical properties of the Alexander invariant. This seems to be true, which suggests that some classical construction should account for these quantum invariants. I will mainly focus on the two different techniques that were used to obtain the evaluations.  
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23 March 2017 14:1515:15 
Jens Hoppe KTH, Stockholm 
Quantized minimal surfaces  HG G 19.1  
30 March 2017 15:1516:15 
Robert Seiringer IST Austria 
Stability of quantum manybody systems with point interactions  HG G 43  
Abstract: We present a proof that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m∗. The value of m∗ is independent of N and turns out to be less than 1. This fact is of relevance for the stability of fermionic gases in the unitary limit. We also present a rigorous version of the Tan relations valid for all wave functions in the domain of the Hamiltonian of this model.  
6 April 2017 15:1516:15 
Dev Sinha University of Oregon 
A program to construct integervalued finitetype knot invariants  HG G 43  
Abstract: Using techniques closely related to his celebrated work in deformation theory, Kontsevich constructed an explicit, geometric universal Vassiliev invariant over the real numbers (or by deep results, over the rational numbers). Vassiliev invariants over the integers are far from settled. We outline a program to investigate them using the GoodwillieWeiss tower for the embedding functor. We recently showed this tower has needed structure and provided spectral sequence evidence for the conjecture that the tower serves as a universal finitetype invariant over the integers. We have also developed Hopf invariants for homotopy groups and now more general mapping sets, which have the potential to detect components of the tower. We describe these two lines of progress and then ideas for next steps.  
11 May 2017 15:1516:15 
Giovanni Felder ETH Zürich 
Equivariant elliptic cohomology and elliptic quantum groups  HG G 43  
Abstract: I will report on joint work with R. Rimanyi and A. Varchenko. We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on weight functions and shuffle products. We obtain an action of the dynamical elliptic quantum groups by difference operators on certain modules over the equivariant elliptic cohomology.  
10 July 2017 15:0017:00 
Xin Fang Universität Köln 
Toric degenerations of flag varieties via NewtonOkounkov bodies  HG G 43  
Abstract: Toric degenerations translate geometric properties of varieties to combinatorial ones of polytopes or cones. In this talk I will introduce a general framework to construct toric degenerations of flag varieties via birational sequences and NewtonOkounkov bodies. This talk is based on joint works with Ghislain Fourier and Peter Littelmann.  
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24 July 2017 14:1515:15 
Boris Tsygan Northwestern 
Notes on operations on Hochschild chains  HG G 43  
Abstract: Hochschild chains of an associative algebra are a noncommutative generalization of differential forms on a manifold. As such, they might be expected to possess an algebraic structure similar to one that exists on forms. They do indeed carry some of it, notably an analog of the De Rham differential, and fail to carry other structure, such as the cup product. We will discuss the (hidden) traces of the product and of a BV structure that they do have. In particular we will define the notion of a Hamiltonian action of a Hopf algebra. The exposition will be based in part on the GinzburgSchedler approach to Hochschild and cyclic homology. 
Archive: AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11
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