Past Programs

Speaker: Cheuk-Yu Mak (Cambridge University)

Title: Discrete Legendre transform and tropical multiplicity from symplectic geometry

Abstract:
There is a long history of enumerative invariants and related problems in mirror symmetry. One powerful approach to understand it is given by counting tropical curves with multiplicities. Tropical multiplicity formula in dimension two can be easily understood but the generalization to higher dimensions is less transparent. In this talk, we explain the relation between tropical multiplicities and the torsion of the first homology group of the associated Lagrangian submanifolds/cell complexes. It is a preparation talk for the talk "Tropically constructed Lagrangians in mirror quintic threefolds", which explains the construction of associated Lagrangian submanifolds using degeneration of hypersurface in toric orbifold.
It is a joint work with Helge Ruddat.

The workshop on additive combinatorics will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

Co-organizers of this workshop include Venkat Guruswami, Alexander Barg, Mary Wootters. More details about this event, including participants, will be updated soon.

More details can be found here: Workshop Webpage

Speaker: Brandon B. Meredith (Embry-Riddle Aeronautical University)

Title: Mirror Symmetry on Toric Surfaces via Tropical Geometry

Abstract:
Mirror symmetry is a curious duality, first noticed by physicists and then excitedly embraced by mathematicians, between certain manifolds and their "mirror" spaces. This talk considers mirror symmetry on toric surfaces, which are varieties with certain convenient combinatorial properties and include many well-known surfaces. These surfaces are especially suited to being exploited by tropical geometry, which is a form of algebraic geometry over the "tropical semi-ring." This talk will discuss the generalization of mirror symmetry to all toric surfaces (expanded from just the Fano case) following the Gross-Siebert Program wherein singularities are added to the tropical picture in order to pull more curves into view.

The workshop on additive combinatorics will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

Co-organizers of this workshop include Venkat Guruswami, Alexander Barg, Mary Wootters. More details about this event, including participants, will be updated soon.

More details can be found here: Workshop Webpage

Speaker: Mauricio Romo (IAS)

Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications

Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

The workshop on additive combinatorics will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

Co-organizers of this workshop include Venkat Guruswami, Alexander Barg, Mary Wootters. More details about this event, including participants, will be updated soon.

More details can be found here: Workshop Webpage

The workshop on additive combinatorics will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

Co-organizers of this workshop include Venkat Guruswami, Alexander Barg, Mary Wootters. More details about this event, including participants, will be updated soon.

More details can be found here: Workshop Webpage

Speaker: Mauricio Romo (IAS)

Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications

Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

The workshop on additive combinatorics will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

Co-organizers of this workshop include Venkat Guruswami, Alexander Barg, Mary Wootters. More details about this event, including participants, will be updated soon.

More details can be found here: Workshop Webpage

Fabian Haiden (Harvard)

Title: Geometric flows, iterated logarithms, and balanced weight filtrations

Friday, April 13, 2018, at 11:00am-12:00pm in Science Center 530

Abstract: The long term behavior of certain gradient flows, both finite and infinite dimensional, is governed by an algebraically defined balanced weight-type filtration which provides a canonical refinement of the Harder-Narasimhan filtration. In recent joint work with Katzarkov, Kontsevich, and Pandit ( arXiv:1802.04123 ) we consider in detail the case of the Yang-Mills flow on the space of metrics on a holomorphic bundle over a Riemann surface, as well as a modified curve shortening flow on the cylinder. I will discuss these results and conjectural generalizations.

Speaker: Yuan Gao (Stony Brook University)

Time and Venue: April/16th(Mon) 12pm - 1pm, G10 CMSA

Title: On the extension of the Viterbo functor

Abstract: In this talk I will describe deformations of wrapped Fukaya categories that arise from cobordisms, using which the Viterbo restriction functor can be extended to any exact cylindrical Lagrangian submanifold. I will also discuss how this extension can be viewed from the perspective of Lagrangian correspondences.

Alex Teytelboym
(University of Oxford)

Title: Targeted Carbon Tax Reforms

Abstract: We show that in the presence of intersectoral linkages targeted sectoral carbon taxes might be a more effective way of reducing emissions than economy-wide carbon pricing. A carbon tax imposed on all sectors unambiguously reduces aggregate emissions, but taxes targeted at the set of key sectors can lead to the greatest emissions reduction. Due to intersectoral linkages and a tax rebate effect, taxing non-key sectors dampens the reduction in aggregate emissions. A key sector typically not only produces a lot of emissions, but also has a large influence on emissions in the rest of the economy. We focus on incremental changes in carbon taxes—carbon tax reforms—to characterise the set of key sectors analytically.

Speaker: Yefeng Shen (University of Oregon)

Time and Venue: April/17 (Tues) 12:30pm - 1:30pm, G02 CMSA

Title: LG/CY correspondence for Fermat elliptic curves

Abstract:
We use holomorphic Cayley transformations of quasi-modular forms to realize a correspondence between Fan-Jarvis-Ruan-Witten invariants of the Fermat cubic polynomial and Gromov-Witten invariants of elliptic curves at all genus. Use tautological relations, we know the building blocks in both theories are just genus one invariants. The latter are governed by a Chazy equation, by using Belorousski-Pandharipande’s relation on \bar{M}_{2,3}. The modular properties essentially follow from the Chazy equation and the initial values in FJRW theory can be calculated by Chang-Li-Li's cosection localization. This work is joint with J. Li and J. Zhou.

Ravi Jagadeesan
(Harvard University)

Title: Optimal income taxation with growth effects

Abstract: I analyze redistributive optimal capital and labor income taxation in endogenous growth models with heterogeneous agents. The government faces a dynamic equity-efficiency trade-off between redistribution, static distortions, and growth effects. Positive capital income taxation can be optimal, and the redistributive component of the optimal capital income tax is always positive. With optimal capital income taxation, the optimal marginal labor income tax rates are systematically lower than their static values. My results apply in the AK growth model and in a reduced-form endogenous growth framework that nests models of growth via expanding varieties and Schumpterian growth models.