## FRG Worshop: Recent Progress in String Theory and Mirror Symmetry

To help us organize the workshop activities, food and drinks, please complete the registration form if you are likely to attend.

### Preliminary Program Schedule

Time Friday March 6 Saturday March 7
9:30-10:30 Nikita Nekrasov
11:00-12:00 Chris Beasley Ronen Plesser
12:00-1:30 lunch break lunch break
1:30-2:30 Greg Moore Dave Morrison
3:00-4:00 Cyril Closset Wati Taylor
4:30-5:30 Ilarion Melnikov Jie Zhou
6:00-8:00 reception banquet* at Mulan

### Due to their flight cancellations, some speakers unfortunately could not make it in time, and some of the talks have to be rescheduled or cancelled. The first talk Friday morning by Chris Beasley will start at 10:30am. We will update the workshop program as information comes in. Please stay tuned. We apologize for any inconvenience due to the rescheduling.

• All Lectures will be held in Abelson Building Rm 333.
• Directions to Brandeis, Abelson Building.
• Mulan Taiwanese Restaurant: 835 Main St, Waltham, MA 02451. (781) 642-9263.
• Numbers for cabs in Waltham: WalthamTaxi 781-647-1117; Patriot Taxi 781-301-1322;
Waltham Cool Ride 781-647-8294.
• *If you would like to attend the banquet at Mulan, please give your name to our conference coordinator Catherine Broderick. There will be a $10 copay (if you are not an invited speaker). Catherine will be in Abelson 333 at noon, Friday. You can also find her in Goldsmith 216 (a building adjacent to Abelson) between 1:30-4:30pm on Friday. ### Invited Lectures ### Chris Beasley Northeastern University Title: Supersymmetry and Legendrian Knots Abstract:I will discuss a new class of supersymmetric Wilson loop operators in pure N=2 Yang-Mills-Chern-Simons theory. These Wilson loops preserve one supercharge on-shell and wrap arbitrary Legendrian knots in the standard contact R^3. As time permits, I will present aspects of the perturbative and non-perturbative analysis of these operators. Lecture notes ### Katrin Becker Texas A&M Title: M-theory and G2 manifolds Abstract: The uplift of classical solutions of M-theory to the quantum theory will be discussed. ### Cyril Closset Simons Center Title: Curved-space supersymmetry and Omega-background for 2d N=(2,2) theories, localization and vortices. Abstract: I will discuss N=(2,2) supersymmetric gauge theories on the sphere with an Omega deformation. In particular, I will explain how to compute Omega-deformed A-type topological correlation functions of GLSMs on the sphere in purely field-theoretic terms (i.e. without relying on a target-space picture), improving on previous techniques. The resulting general formula simplifies previous results in the Abelian (toric) case, while it leads to new results for non-Abelian GLSMs. Lecture notes ### Ilarion Melnikov Harvard University Title: Aspects of (0,2) theories. Abstact: I will give a general overview of recent developments in two-dimensional theories with (0,2) supersymmetry, mainly in the context of critical heterotic strings with supersymmetric vacua but also touching upon other theories and aspects of (0,2) RG flow. Lecture notes ### Greg Moore Rutgers University Title: Interfaces for d=2 N=(2,2) QFTs, and their uses Abstract: This talk describes the web formalism for describing instanton effects in massive d=2 N=(2,2) QFT. (The standard examples we have in mind are Landau-Ginzburg models.) The web formalism shows that these models have spaces of local operators forming L-infinity and A-infinity algebras. Certain "interactions" of BPS solitons and D-branes are described by solutions of the Maurer-Cartan equations in these algebras. Developing a theory of interfaces between different models allows one to formulate a categorified version of certain wall-crossing formulae. At the end, if time permits, I will sketch how interfaces also might be useful in formulating knot homology. This talk is really the second of a 2-part talk. The first part, aimed primarily at physicists, will be my seminar at Harvard on Thursday March 5. The second part will be aimed primarily at mathematicians. I will not assume the audience has been to part one, but I will also not dwell on the physical background motivating the formalism I will explain. Everything in these two talks is extracted from a project with Davide Gaiotto and Edward Witten. Lecture notes ### David Morrison UC Santa Barbara Title: Superconformal field theories in six dimensions Abstract: The past year has seen dramatic progress in the classification of six-dimensional superconformal field theories with minimal supersymmetry. The main tool has been a detailed study of F-theory on a complex surface S which is a small neighborhood of a contractible collection of compact complex curves C_i, where the axio-dilaton profile of F-theory is specified by an elliptic fibration over S. In late 2013, it was shown that contracting the curves C_i on S yields a quotient singularity. More recently, it has been shown the F-theory constructions reproduce an intricate mathematical classification of homomorphisms$\Gamma_{E_8} \to E_8(\mathbb{R})$where$\Gamma_{E_8}\$ is the binary icosahedral group, as expected from a duality with the Horava-Witten model of the heterotic string.
Lecture notes

### Nikita Nekrasov SCGP & IHES

Title: Non-perturbative Dyson-Schwinger equations and BPS/CFT correspondence
Abstract: We report on progress in understanding the non-local symmetries of quantum field theory, notably gauge theory. The symmetries relate topologically distinct sectors of the field space. We study these symmetries in some detail in the context of the BPS/CFT correspondence. To this end we introduce a notion of qq-characters, which generalize the q-characters of quantum affine algebras and Yangians. We show that the qq-characters can be used to derive an infinite set of Dyson-Schwinger type relations obeyed by the supersymmetric partition functions of four dimensional gauge theory (with surface operators), containing the Knizhnik-Zamolodchikov(-Bernard) equations, and Belavin-Polyakov-Zamolodchikov equations.

### Ronen Plesser Duke University

Title: T3 Fibrations for Complete Intersection CY in Toric Varieties
Lecture notes

### Wati Taylor MIT

Title: F-theory and the classification of elliptic Calabi-Yau threefolds
Abstract: Combining the minimal model approach to complex surfaces with physical insights from F-theory provides a systematic approach to the classification of elliptic Calabi-Yau threefolds. This talk will describe these developments, including the enumeration of elliptic Calabi-Yau threefolds with large Hodge number h21. Related progress on the classification of elliptic Calabi-Yau fourfolds will also be described.
Lecture notes

### Jie Zhou Perimeter Institute

Title: Modularity in Gromov-Witten theory
Abstract: I will talk about modularity of the generating functions of Gromov-Witten invariants of some special Calabi-Yau one, three, and perhaps two-folds. I will explain why elliptic modularity is expected in these cases and show that the generating functions are quasi-modular forms by using both A-model and B-model techniques. Some applications of the modularity will also be discussed.
The talk is based on joint works with M. Alim, E. Scheidegger, S.-T. Yau, S.-C-Lau, Y. Ruan and Y. Shen.
Lecture notes

Workshop program will be continually updated as information arrives.
Last updated:
Created: Dec 2014
Current time:
Comments: lian at brandeis dot edu