This seminar features recent results at the intersection of high-energy physics, string theory, and geometry and topology.
Prerequisites: None. Everyone is welcome. To receive announcements for this seminar, and for the advertisement of other talks at the intersection of physics and geometry in Heidelberg, you may subscribe to the Mailing List.
Time and Place: Regularly: Monday, 2 p.m.s.t., MATHEMATIKON
Alternatively: Tuesday or Thursday, 2 p.m.s.t., various locations (or as noted below).
|November 28||John Alexander Cruz Morales (Bonn)||On Stokes matrices for Frobenius manifolds|
|In this talk we will discuss how to compute the Stokes matrices for some semisimple Frobenius manifolds by using the so-called monodromy identity. In addition, we want to discuss the case when we get integral matrices and their relations with mirror symmetry. This is part of an ongoing project with M. Smirnov and previous joint work with Marius van der Put.|
|December 5||Adam Alcolado (McGill)||Extended Frobenius Manifolds|
|Frobenius manifolds, introduced by Dubrovin, are objects which know about many different things in mathematics, for example, the enumeration of rational curves, or the list of platonic solids. We will introduce a generalization of Frobenius manifolds which know about real (or open) enumerative geometry. What else do these extended Frobenius Manifolds know?|
|December 12||Pietro Longhi (Uppsala)||Probing the geometry of BPS states with spectral networks|
|In presence of defects the Hilbert space of a quantum field theory can change in interesting ways. Surface defects in 4d N=2 theories introduce a class of 2d-4d BPS states, which the original 4d theory does not possess. For theories of class S, spectral networks count 2d-4d BPS states, and through the 2d-4d wall-crossing phenomenon the 4d BPS spectrum can be obtained. Adopting this physical viewpoint on spectral networks, I will illustrate some recent and ongoing developments based on this framework, with applications to the study of 2d (2,2) BPS spectra, and of 4d N=2 BPS monodromies.|
|Tuesday, December 13||Michael Bleher (Heidelberg)||Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory|
|In the last decade it was realized that supersymmetric boundary conditions in super Yang-Mills theories can provide invaluable insight into several areas of current mathematical research. Motivated especially by their appearance in a categorification of knot invariants, I will give a short overview on half-BPS boundary conditions in 4d N=4 SYM theory. Of particular interest is the Nahm-pole boundary condition and the main goal will be to review the corresponding moduli space of supersymmetric vacua.|
|January 30||Chris Elliott (IHÉS)||Algebraic Structures for Kapustin-Witten Twisted Gauge Theories|
|Topological twisting is a technique for producing topological field theories from supersymmetric field theories -- one exciting application is Kapustin and Witten's 2006 discovery that the categories appearing in the geometric Langlands conjecture can be obtained as topological twists of N=4 supersymmetric gauge theories, and that these two categories are interchanged by S-duality. There are, however, several incompatibilities between Kapustin and Witten's construction and the geometric representation theory literature. First, their techniques do not produce the right algebraic structures on the moduli spaces appearing in geometric Langlands, and secondly, their construction doesn't explain the singular support conditions Arinkin and Gaitsgory introduced in order to make the geometric Langlands correspondence possible. In this talk I'll explain joint work with Philsang Yoo addressing both of these issues: how to understand topological twisting in (derived) algebraic geometry, and how to interpret singular support conditions as arising from the choice of a vacuum state.|
| Wednesday, February 1
SR B, 2 p.m.s.t.
|Chris Elliott (IHÉS)||An Introduction to the Batalin-Vilkovisky Quantization Formalism|
|February 13||Steven Sivek (Bonn)||The augmentation category of a Legendrian knot|
|Given a Legendrian knot in R3, Shende, Treumann, and Zaslow defined a category of constructible sheaves on the plane with singular support controlled by the front projection of the knot. This category turns out to be equivalent to a unital A∞ category, called the augmentation category, which is defined in terms of a holomorphic curve invariant (Legendrian contact homology) of the knot. In this talk I will describe the construction of these categories and outline a proof that they are equivalent. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Zaslow.|
|February 20||Ben Knudsen (Harvard)||A local-to-global approach to configuration spaces|
|I will describe how ideas borrowed from functorial field theory, the theory of chiral algebras, and BV theory may be profitably adapted to the purely topological problem of calculating Betti numbers of configuration spaces. These methods lead to improvements of classical results, a wealth of computations, and a new and combinatorial proof of homological stability.|
|February 27||Owen Gwilliam (Bonn)||Chiral differential operators and the curved beta-gamma system|
|Chiral differential operators (CDOs) are a vertex algebra analog of the associative algebra of differential operators. They were originally introduced by mathematicians using just sheaf theory and vertex algebraic machinery. Later, Witten explained how CDOs on a complex manifold X arise as the perturbative part of the curved beta-gamma system with target X. I will describe recent work with Gorbounov and Williams in which we construct the BV quantization of this theory and use a combination of factorization algebras and formal geometry to recover CDOs. At the end, I hope to discuss how the techniques we developed apply to a broad class of nonlinear sigma models, including source manifolds of higher dimension.|
|March 20||Michele Cirafici (I.S.T. Lisboa)||Framed BPS quivers and line defects|
|I will discuss a certain class of line defects in four dimensional supersymmetric theories with N=2. I will show that many properties of these operators can be rephrased in terms of quiver representation theory. In particular one can study BPS invariants of a new kind, the so-called framed BPS states, which correspond to bound states of ordinary BPS states with the defect. I will discuss how these invariants arise from framed quivers. Time permitting I will also discuss a formalism to study these quantities based on cluster algebras.|
|May 29||Jon Keating (Bristol)||TBA|