Talks in mathematical physics

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Spring Semester 2017

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Date / Time Speaker Title Location
23 February 2017
15:15-16:15
Wellington Galleas
ETH Zurich
Partition function of the elliptic gl2 SoS model as a single determinant  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.
2 March 2017
15:15-16:15
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 ∈ 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.
* 9 March 2017
14:15-15:15
Ping Xu
Penn State
Formality theorem and Kontsevich-Duflo 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 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.
16 March 2017
15:15-16:15
Ben Kohli

Title T.B.A. HG G 43 
30 March 2017
14:15-15:15
Robert Seiringer

Title T.B.A. tba   
6 April 2017
15:15-16:15
Dev Sinha

Title T.B.A. HG G 43 

Archive: 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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25.02.2017
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