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Frühjahrssemester 2017

Datum / Zeit Referent:in Titel Ort
23. Februar 2017
15:15-16:15 		Wellington Galleas
ETH Zurich
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Talks in Mathematical Physics

Titel Partition function of the elliptic gl2 SoS model as a single determinant
Referent:in, Affiliation Wellington Galleas, ETH Zurich
Datum, Zeit 23. Februar 2017, 15:15-16:15
Ort HG G 43
Abstract Partition functions of vertex models with domain-wall boundaries have appeared in a variety of contexts ranging from enumerative combinatorics to the study of gauge theories. The six-vertex 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 six-vertex model. The next natural candidate for this study is the elliptic gl2 Solid-on-Solid (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 Yang-Baxter 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.
Partition function of the elliptic gl2 SoS model as a single determinantread_more
HG G 43
2. März 2017
15:15-16:15 		Alexander Veselov
Loughborough University
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Talks in Mathematical Physics

Titel Lyapunov spectrum for Markov dynamics and hyperbolic structures
Referent:in, Affiliation Alexander Veselov, Loughborough University
Datum, Zeit 2. März 2017, 15:15-16:15
Ort HG G 43
Abstract We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x ∈ RP1 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 ΛX 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.
Lyapunov spectrum for Markov dynamics and hyperbolic structuresread_more
HG G 43
* 9. März 2017
14:15-15:15 		Ping Xu
Penn State University
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Talks in Mathematical Physics

Titel Formality theorem and Kontsevich-Duflo theorem for Lie pairs
Referent:in, Affiliation Ping Xu, Penn State University
Datum, Zeit 9. März 2017, 14:15-15:15
Ort 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 L-infinity 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 Kontsevich-Duflo 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 Hsuan-Yi Liao and Mathieu Stienon.
Formality theorem and Kontsevich-Duflo theorem for Lie pairsread_more
HG G 19.1
16. März 2017
15:15-16:15 		Ben Kohli
Université de Bourgogne
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Talks in Mathematical Physics

Titel The Links-Gould invariants seen as generalizations of the Alexander polynomial
Referent:in, Affiliation Ben Kohli, Université de Bourgogne
Datum, Zeit 16. März 2017, 15:15-16:15
Ort HG G 43
Abstract The Links-Gould invariants are a family of two variable quantum link isotopy invariants. They are derived from Hopf superalgebras U_q(gl(m|n)). However we now know that the Alexander invariant can be obtained through several different evaluations from the Links-Gould polynomial,using work by De Wit-Ishii-Links, and more recently joint work with Bertrand Patureau-Mirand. Therefore all the information contained in the Alexander polynomial can be found inside the Links-Gould invariants, including the homological information: lower bound for the genus, criterion for fiberedness of knots, ... So we can wonder whether the Links-Gould 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.
The Links-Gould invariants seen as generalizations of the Alexander polynomialread_more
HG G 43
* 23. März 2017
14:15-15:15 		Jens Hoppe
KTH, Stockholm
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Talks in Mathematical Physics

Titel Quantized minimal surfaces
Referent:in, Affiliation Jens Hoppe, KTH, Stockholm
Datum, Zeit 23. März 2017, 14:15-15:15
Ort HG G 19.1
Quantized minimal surfaces
HG G 19.1
30. März 2017
15:15-16:15 		Robert Seiringer
IST Austria
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Talks in Mathematical Physics

Titel Stability of quantum many-body systems with point interactions
Referent:in, Affiliation Robert Seiringer, IST Austria
Datum, Zeit 30. März 2017, 15:15-16:15
Ort 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.
Stability of quantum many-body systems with point interactionsread_more
HG G 43
6. April 2017
15:15-16:15 		Dev Sinha
University of Oregon
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Talks in Mathematical Physics

Titel A program to construct integer-valued finite-type knot invariants
Referent:in, Affiliation Dev Sinha, University of Oregon
Datum, Zeit 6. April 2017, 15:15-16:15
Ort 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 Goodwillie-Weiss 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 finite-type 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.
A program to construct integer-valued finite-type knot invariantsread_more
HG G 43
11. Mai 2017
15:15-16:15 		Giovanni Felder
ETH Zürich
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Talks in Mathematical Physics

Titel Equivariant elliptic cohomology and elliptic quantum groups
Referent:in, Affiliation Giovanni Felder, ETH Zürich
Datum, Zeit 11. Mai 2017, 15:15-16:15
Ort 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.
Equivariant elliptic cohomology and elliptic quantum groupsread_more
HG G 43
10. Juli 2017
15:00-17:00 		Xin Fang
Universität Köln
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Talks in Mathematical Physics

Titel Toric degenerations of flag varieties via Newton-Okounkov bodies
Referent:in, Affiliation Xin Fang, Universität Köln
Datum, Zeit 10. Juli 2017, 15:00-17:00
Ort 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 Newton-Okounkov bodies. This talk is based on joint works with Ghislain Fourier and Peter Littelmann.
Toric degenerations of flag varieties via Newton-Okounkov bodiesread_more
HG G 43
* 24. Juli 2017
14:15-15:15 		Boris Tsygan
Northwestern
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Talks in Mathematical Physics

Titel Notes on operations on Hochschild chains
Referent:in, Affiliation Boris Tsygan, Northwestern
Datum, Zeit 24. Juli 2017, 14:15-15:15
Ort 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 Ginzburg-Schedler approach to Hochschild and cyclic homology.
Notes on operations on Hochschild chainsread_more
HG G 43

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