The topic of the talks are as follows:
Date  Title  Abstract 
332017  Modularity of DT invariants on smooth K3 fibrations I  Motivated by Sduality modularity conjectures in string theory, we study the DonaldsonThomas invariants of 2dimensional sheaves inside a nonsingular threefold X. Our main case of study is when X is given by a smooth surface fibration over a curve with the canonical bundle of X pulled back from the base curve. We study the DonaldsonThomas invariants, as defined by Richard Thomas, of the 2dimensional Gieseker stable sheaves in X supported on the fibers. In case whereXis aK3 fibration, analogous to the GromovWitten theory formula established by MaulikPandharipande, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the fiber and the NoetherLefschetz numbers of the fibration, and prove that the invariants have modular properties. We are intending to go through these lectures with a relatively slow speed, that is: TheoremProof style, (so we will be less handwavy!) and we intend to establish some of the required background, e.g NoetherLefschetz theory, vector valuedmodular forms etc. 
382017  Modularity of DT invariants on smooth K3 fibrations II  Motivated by Sduality modularity conjectures in string theory, we study the DonaldsonThomas invariants of 2dimensional sheaves inside a nonsingular threefold X. Our main case of study is when X is given by a smooth surface fibration over a curve with the canonical bundle of X pulled back from the base curve. We study the DonaldsonThomas invariants, as defined by Richard Thomas, of the 2dimensional Gieseker stable sheaves in X supported on the fibers. In case whereXis aK3 fibration, analogous to the GromovWitten theory formula established by MaulikPandharipande, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the fiber and the NoetherLefschetz numbers of the fibration, and prove that the invariants have modular properties. We are intending to go through these lectures with a relatively slow speed, that is: TheoremProof style, (so we will be less handwavy!) and we intend to establish some of the required background, e.g NoetherLefschetz theory, vector valued modular forms etc. 
3102017  Conifold Transitions and modularity of DT invariants on Nodal fibrations 
Following lectures I and II we continue the discussion on the moduli space of shaves with two dimensional support on K3fibered threefolds, which can admit finitely many nodal (rational double point singularity at worst) fibers. We will use the conifold transitions and degeneration techniques in this case to relate the geometry of our moduli space and its enumerative invariants to the ones studied in lectures I, II over smooth K3fibrations.

452017  Stable pair PT invariants on smooth fibrations I  We study PandharipandeThomas’s stable pair theory on smooth K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of KawaiYoshioka’s formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and NoetherLefschetz numbers of the fibration. 
472017  Stable pair PT invariants on smooth fibrations II

We study PandharipandeThomas’s stable pair theory on smooth K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of KawaiYoshioka’s formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and NoetherLefschetz numbers of the fibration. 
4122017  Stable pair PT invariants on nodal fibrations: perverse sheaves, Wallcrossings, and an analog of fiberwise Tduality  Following lecture 4, we continue the study of stable pair invariants of K3fibered threefolds., We investigate the relation of these invariants with the perverse (noncommutative) stable pair invariants of the K3fibration. In the case that the fibration is a projective CalabiYau threefold, by means of wallcrossing techniques, we write the stable pair invariants in terms of the generalized DonaldsonThomas invariants of 2dimensional Gieseker semistable sheaves supported on the fibers. 
4142017  DT versus MNOP invariants and S_duality conjecture on general complete intersections  Motivated by Sduality modularity conjectures in string theory, we define new invariants counting a restricted class of twodimensional torsion sheaves, enumerating pairs Z⊂H in a Calabi–Yau threefold X. Here H is a member of a sufficiently positive linear system and Z is a onedimensional subscheme of it. The associated sheaf is the ideal sheaf of Z⊂H, pushed forward to X and considered as a certain Joyce–Song pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X. 
4192017  Proof of Sduality conjecture on quintic threefold I  I will talk about an algebraicgeometric proof of the Sduality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic CalabiYau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasiprojective surface is a modular form. This is a generalization of the result of OkounkovCarlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of NoetherLefschetz numbers as I will explain, will provide the ingredients to achieve an algebraicgeometric proof of Sduality modularity conjecture. 
4282017  Proof of Sduality conjecture on Quintic threefold II  I will talk about an algebraicgeometric proof of the Sduality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic CalabiYau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasiprojective surface is a modular form. This is a generalization of the result of OkounkovCarlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of NoetherLefschetz numbers as I will explain, will provide the ingredients to achieve an algebraicgeometric proof of Sduality modularity conjecture. 
The list of speakers is below and will be updated as details are confirmed.
Date  Name  Title 
091516  
092216  Netanel Blaier, Brandeis  “Intro to HMS.”
Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the Aside (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants. 
092916  Netanel Blaier, Brandeis  “Intro to HMS 2.”
Abstract: In the second talk, we review (some) of the nittygritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of Jholomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’. 
100616 
Hansol Hong, CMSA

Title: Homological mirror symmetry for elliptic curves
Abstract: 
101316 
YuWei Fan, Harvard 
Title: Semiflat mirror symmetry and FourierMukai transform Abstract: We will review the semiflat mirror symmetry setting in StromingerYauZaslow, and discuss the correspondence between special Lagrangian sections on the Aside and deformed HermitianYangMills connections on the Bside using real FourierMukai transform, following LeungYauZaslow. 
102016 
Tim Large, MIT 
Title: “Symplectic cohomology and wrapped Fukaya categories”
Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to noncompact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an Ainfinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closedstring counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the Bside of mirror symmetry, to turning on a LandauGinzburg potential. 
102716 
Philip Engel, Columbia 
Title: Mirror symmetry in the complement of an anticanonical divisor” According to the SYZ conjecture, the mirror of a CalabiYau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open CalabiYau variety XD given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in XD, and note that it locally has the structure of a CalabiYau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs. 
110316 
Yusuf Baris Kartal, MIT 
I will present AurouxKatzarkovOrlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LGmodels together with Bfields. I plan to show how the general Bfield corresponds to noncommutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc. 
111016  No seminar this week  
120816 
Lino Amorim, Boston University 
Title: The Fukaya category of a compact toric manifold Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of FukayaOhOhtaOno. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror. 
121516 
Siu Cheong Lau, University of Missouri 
Date  Name  Title/Abstract 
020717  Nikhil Naik, Harvard/MIT  Title: Visual Urban Sensing: Understanding Cities with Computer Vision
Abstract: Street View services have documented the visual appearance of cities from more than a hundred countries across the world in the past decade. I design computer vision tools that harness Street View imagery to conduct computerdriven automated surveys of the built environment at streetlevel resolution and global scale. In this talk, I will describe two algorithms that computationally evaluate urban appearance from imagery. The first algorithm, Streetscore, quantifies the perceived safety of a street block, by harnessing data from a crowdsourced game. The second algorithm quantifies the growth or decay of cities from timeseries Street View imagery obtained over several years. Finally, I will demonstrate the use of these algorithms for studying important questions in urban economics, sociology, and urban planning. 
021417  Mauricio Fernández Duque, Harvard  Title: Pluralistic Ignorance and Preference Complementarities
Abstract: I develop a theory of group interaction with preference complementarities, in which individuals know that others privately judge whether their type matches that of the majority in the group. The model sheds light on situations of pluralistic ignorance — a social situation where `a majority of group members privately reject a norm, but incorrectly assume that most others accept it, and therefore go along with it.’ (Katz and Allport, 1931). As opposed to past approaches, our model explains three stylized facts of pluralistic ignorance: that most individuals are acting reluctantly, that they think most others are not acting reluctantly, and that an inefficient equilibrium can be sustained in which most are reluctantly cooperating. We show some preliminary results suggesting that as the certainty over the population distribution of preferences grows, the probability of pluralistic ignorance increases when group size is small and decreases when group size is large. 
022117  Ravi Jagadeesan, Harvard 
Title: Complementary inputs and the existence of stable outcomes in large trading networks Abstract: This paper studies a model of large trading networks with bilateral contracts. The model allows income effects, unlike in parts of the matching literature, and imperfectly tradeable goods, unlike in the general equilibrium literature. In our setting, under standard continuity and convexity conditions, a stable outcome is guaranteed to exist in any acyclic network, as long as all firms regard sales as substitutes and the market is large. Thus, complementarities between inputs do not preclude the existence of stable outcomes in large markets. Even when there are complementarities between sales, this paper shows that tree stable outcomes are guaranteed to exist in large markets, under continuity and convexity conditions. The model presented in this paper generalizes and unifies versions of general equilibrium models with divisible and indivisible goods, matching models with continuously divisible contracts, models of large (twosided) matching with complementarities, and club formation models. Additional results provide intuition for the role of unidirectional substitutability conditions and acyclicity in the main existence results, and explain what kinds of equilibria are guaranteed to exist even when these conditions are relaxed. Unlike in twosided largemarket settings, the sufficient conditions described in this paper pin down maximal domains for the existence of equilibria. 
030717  Krishna Pendakur, Simon Fraser University

Title: Infant Mortality and the Repeal of Federal Prohibition
Abstract: Exploiting a newly constructed dataset on countylevel variation in prohibition status, this paper asks two questions: what were the effects of the repeal of federal prohibition on infant mortality? And were there any significant externalities from the individual policy choices of counties and states on their neighbors? We find that dry counties with at least one wet neighbor saw baseline infant mortality increase by roughly 3%. We argue that such crossborder policy externalities are plausibly exogenous sources of variation in assessing the effects of prohibition’s repeal and should be a key consideration in the contemporary policy debate on the prohibition of illicit substances. 
031417 
Spring Break — NO SEMINAR


032117  Danielle Li, Harvard  Title: Financing Novel Drugs
Abstract: The process of drug discovery is expensive and highly uncertain. Because of this, riskaverse firms facing financial constraints may be less likely to invest in novel drugs than may be socially optimal. We examine this hypothesis by studying how resource constraints impact firms’ decisions to invest in novel drug compounds. This paper has two contributions. First, we develop a new moleculebased measure of the chemical novelty of new drug candidates. Second, we use variation in the expansion of Medicare prescription drug coverage in the United States (which differentially benefited firms with more drugs targeted toward the elderly, as well as firms with more remaining market exclusivity on those drugs) to isolate exogenous variation in cash flow to firms. We find that firms which benefit more from the expansion of drug coverage develop more drug candidates as a result and, moreover, this increase is driven by an increase in the development of more chemically novel drug compounds. 
041117  Jann Speiss, Harvard  Title: Integrating Machine Learning into Applied Econometrics
Abstract: Machine learning focusses on highquality prediction rather than on unbiased parameter estimation, limiting its direct use in typical program evaluation applications in economics. Still, many tasks that we think of estimation problems have implicit prediction components. In this talk, I (1) lay out some basic features and limitations of machine learning; (2) propose a framework for integrating it into estimation tasks; and (3) work out two examples from experimental analysis to highlight my approach: accounting for control variables, and testing effects on multiple outcomes. 
041217  Alex Teytelboym, Oxford

Title: Refugee Resettlement
Abstract: Over 100,000 refugees are permanently resettled from refugee camps to hosting countries every year. Nevertheless, refugee resettlement processes in most countries are ad hoc, accounting for neither the priorities of hosting communities nor the preferences of refugees themselves. Building on models from two sided matching theory, we introduce a new framework for matching with multidimensional constraints that models refugee families’ needs for multiple units of different services, as well as the service capacities of local areas. We propose several refugee resettlement mechanisms that can be used by hosting countries under various institutional and informational constraints. Our mechanisms can improve match efficiency, incentivize refugees to report where they would like to settle, and respect priorities of local areas thereby encouraging them to accept more refugees overall. Beyond the refugee resettlement context, our model This seminar will run from 4:005:00pm 
041817  Battal Doğan, University of Lausanne  Title: A precise representation of acceptant and substitutable choice rules
Abstract: Acceptant and substitutable choice rules have been useful in market design particularly because they guarantee stability and allow for achieving various design objectives such as diversity. What is known from the literature is that each such choice rule has a “collected maximal representation”: there exists a list of priority orderings such that at each choice set, collecting the maximizers of the priority orderings retrieves the choice. For each acceptant and substitutable choice rule, we provide the minimum size collected maximal representation. We show that “responsive choice rules” render a collected maximal representation of the largest size among all acceptant and substitutable choice rules. 
050217  Mohammad Akbarpour, Stanford  Title: Dynamic matching on stochastic networks
Abstract: Motivated by the problem of paired kidney exchange, we introduce a dynamic version of the problem of maximum matching in a random network, where agents arrive and depart stochastically, and the composition of the trade network depends endogenously on the matching algorithm. We show that if the planner can identify agents who are about to depart, then waiting to thicken the market is highly valuable, and if the planner cannot identify such agents, then matching agents greedily is close to optimal. The planner’s decision problem in our model involves a combinatorially complex state space. However, we show that simple local algorithms that choose the right time to match agents, but do not exploit the global network structure, can perform close to complex optimal algorithms. 
Date  Name  Title 
02/29/2016  Scott Kominers (Harvard Society of Fellows)  Title: Patent Trolls: Evidence from Targeted Firms

03282016  Mike Luca (Harvard Business School)  
04042016  Lauren Cohen (Harvard Business School)  Title: Playing Favorites: How Firms Prevent the Revelation of Bad News

04182016  Annie Liang  Title: The Theory is Predictive, but is it Complete? An Application to Human Perception of Randomness (with Jon Kleinberg and Sendhil Mullainathan)

110116  Jakub Redlicki, Oxford  Title: What Drives Regimes to Manipulate Information: Criticism, Collective Action, and Coordination
Abstract: Authoritarian states often manipulate information in order to prevent regime change. The model uses the global games framework in which the regime is overthrown if enough citizens attack, however, the citizens are imperfectly informed about its strength and the regime can increase noise in their private information. Inspired by empirical findings in political science (King, Pan and Roberts, 2013; 2014; 2016), this paper illuminates (i) why regimes may aim to prevent collective action rather than criticism of the state per se, and (ii) why they might distract their citizens rather than try to persuade them. Unlike boosting the apparent strength by adding a bias, manipulating the noise is effective even if (i) the citizens can observe the regime’s manipulative action and (ii) the regime is no better informed about its strength than they are. I show that under these conditions the regime has no incentives to increase noise for the purpose of improving the citizen’s perception of the state per se. At the same time, minimising the size of all collective attacks may be an effective way of preventing regime change, especially when the citizens’ private information is intrinsically imprecise. Finally, I demonstrate that if citizens can coordinate better only at the cost of impeded information aggregation, the regime’s incentives to increase noise may become stronger. 
110816  Sifan Zhou, Harvard  Title: NonCompete Agreements and the Career of PhDs.
Abstract: Noncompete agreements are legal contracts that employers use to restrain exemployees from joining another firm or starting a new business in competition against them. While noncompete agreements protect employers’ investments in R&D and human capital, such protection may come at the costs of employees. I study the effects of noncompete agreements on doctorate recipients by analyzing the timeseries and crosssectional variations in the enforceability of these contracts in the United States. Using a differenceindifference approach, I find that, for PhDs who work in the forprofit sector, tougher enforcement decreases their withinstate job mobility. The reduced withinstate job mobility is in part compensated by an increase in job changing across state borders, in line with the situation that noncompete agreements are more difficult to enforce across jurisdictions. Tougher enforcement also slows down the salary growths of these PhDs, consistent with a model in which general human capital is turned in to firmspecific human capital and workers lose bargaining power as they cannot threaten to leave for an outside offer. What is more, freshly minted PhDs are less likely to stay working in the state from which they received their degrees if the state has tougher enforcement. All these effects are consistently strong for engineering majors and less so for life sciences majors. 
111516  Ben Roth, MIT  Title: Keeping The Little Guy Down: A Debt Trap For Informal Lending
Abstract: Microcredit and other forms of informal finance have so far failed to catalyze business growth among small scale entrepreneurs in the developing world, despite their high return to capital. This prompts a reexamination of the special features of informal credit markets that cause them to operate inefficiently. We present a theory of informal lending that highlights two of these features. First, borrowers and lenders bargain not only over division of surplus but also over contractual flexibility (the ease with which the borrower can invest to grow her business). Second, when the borrower’s business becomes sufficiently large she exits the informal lending relationship and enters the formal sector – an undesirable event for her informal lender. We show that in Stationary Markov Perfect Equilibrium these two features lead to a poverty trap and study its properties. The theory facilitates reinterpretation of a number of empirical facts about microcredit: business growth resulting from microfinance is low on average but high for businesses that are already relatively large, and microlenders have experienced low demand for credit. The theory features nuanced comparative statics which provide a testable prediction and for which we establish novel empirical support. Using the Townsend Thai data and plausibly exogenous variation to the level of competition Thai money lenders face, we show that as predicted by our theory, money lenders in high competition environments impose fewer contractual restrictions on their borrowers. We discuss robustness and policy implications. 
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2017 Fall Semester:
Date……….  Name  Title/Abstract 
090417  No Talk  
09112017  YuShen Lin
(Harvad CMSA) 
From the Decomposition of PicardLefschetz Transformation to Tropical Geometry
Abstract: PicardLefschetz transformation tells the monodromy of a fibration with “good” singular fibres. In the case of fibres are Lagrangian in a symplectic $4$manifold, there is a natural decomposition of PicardLefschetz transformation into two elementary transformations from Floer theory. The idea will help to develop the tropical geometry for some hyperKahler surfaces. 
091817  Yoosik Kim
(Boston University) 
Monotone Lagrangian tori in cotangent bundles.
Abstract: As an attempt to classify Lagrangian submanifolds and due to their importance in Floer theory, monotone Lagrangian tori have been got attention. In this talk, we provide a way producing monotone Lagrangian tori in the cotangent bundles of some manifolds including spheres or unitary groups. The construction is based on the classification of Lagrangian fibers of a certain completely integrable system on a partial flag manifolds of various types. We then discuss when their Floer cohomologies (under a certain deformation by nonunitary flat line bundles) do not vanish. This talk is based on joint work with Yunhyung Cho and YongGeun Oh. 
092717  YuWei Fan
(Harvard) 
WeilPetersson geometry on the space of Bridgeland stability conditions
Abstract: Inspired by mirror symmetry, we define WeilPetersson geometry on the space of Bridgeland stability conditions on a CalabiYau category. The goal is to further understand the stringy Kahler moduli space of CalabiYau manifolds. This is a joint work with A. Kanazawa and S.T. Yau. 
100417  Dingxin Zhang
(Brandeis) 
<1 part of slopes under degeneration
Abstract: For a smooth family of projective varieties over a field of characteristic p > 0, it is known that the Newton polygon of fibers goes up under specialization. In this talk, we will show that when the family acquires singular members, the less than one part of the slopes of the Newton polygon goes up under specialization. This could be viewed as a characteristic p analogue of a simple phenomenon in Hodge theory. 
101117  No Talk  
10182017  Nati Blaier
(Harvard CMSA) 
Geometry of the symplectic Torelli group
Abstract: This talk has two parts. In the first part of the talk, I will introduce the group of symplectomorphism and try to convince you that it is a very important object in symplectic topology by surveying some known structural results and drawing a comparison with the situation in the smooth and Kahler geometries as well as the world of lowdimensional topology. In the second part, I’ll discuss the symplectic Torelli group for higher dimensional symplectic manifolds, and an ongoing project to use GromovWitten theory to detect interesting elements. 
10232017
*Monday* 
Florian Beck
(Universität Hamburg) 
Hitchin systems in terms of CalabiYau threefolds.
Abstract: Integrable systems are often constructed from geometric and/or Lietheoretic data. Two important example classes are Hitchin systems and CalabiYau integrable systems. A Hitchin system is constructed from a compact Riemann surface together with a complex Lie group with mild extra conditions. In contrast, CalabiYau integrable systems are constructed from a priori purely geometric data, namely certain families of CalabiYau threefolds. Despite their different origins there is a nontrivial relation between Hitchin and CalabiYau integrable systems. More precisely, we will see in this talk that any Hitchin system for a simplyconnected or adjoint simple complex Lie group is isomorphicto a CalabiYau integrable system (away from singular fibers). 
11012017
*12:30pm1:30pm* 
Chenglong Yu
(Harvard Math) 
PicardFuchs systems of zero loci of vector bundle sections
Abstract: We propose an explicit construction for PicardFuchs systems of zero loci of vector bundle sections. When the vector bundle admits large symmetry, the system we constructed is holonomic. This is a joint work with Huang, Lian and Yau. 
11062017
*Monday* 
Pietro Benetti Genolini(Univ. of Oxford)  Topological AdS/CFT
Abstract: I will describe a holographic dual to the DonaldsonWitten topological twist of gauge theories on a Riemannian fourmanifold. Specifically, I will consider asymptotically locally hyperbolic solutions to Romans’ gauged supergravity in five dimensions with the fourmanifold as conformal boundary, and show that the renormalised supergravity action is independent of the choice of boundary metric. This is a first step in the direction of combining topological quantum field theory with the AdS/CFT correspondence. 
11132017
*Monday 12:30pm* *Room G02* 
Yusuf Baris Kartal(MIT)  Dynamical invariants of categories associated to mapping tori
Abstract: One can construct the symplectic mapping torus for a given a symplectic manifold with a symplectomorphism and use the flux invariant to distinguish the mapping tori of maps of different order. The essential argument is that the flow in a certain direction have different periods depending on the order of the symplectomorphism. In this talk, we will introduce an abstract categorical version of the mapping torus associated to an $A_\infty$ category and an autoequivalence. Then, we will construct a family of bimodules analogous to the flow and discuss how to characterize it intrinsically and how to use it to distinguish different categorical mapping tori. 
11222017  No Talk  
11292017  Amitai Zernik
(IAS) 
Computing the A∞ algebra of RP2m CP2m using open fixedpoint localization.
Abstract: I’ll explain how to compute the equivariant quantum A∞ algebra A associated with the Lagrangian embedding of RP2m in CP2m, using a new fixedpoint localization technique that takes into account contributions from all the corner strata. It turns out that A is rigid, so its structure constants are independent of all choices. When m = 1 and in the nonequivariant limit, they specialize to give Welschinger’s counts of real rational planar curves passing through some generic, conjugation invariant congurations of points in CP2m. So we get a diagrammatic expression for computing Welschinger invariants, which I’ll demonstrate with some examples.Time permitting, I’ll discuss a formal extension to higher genus which satises string and dilaton. 
12062017  Sarah Venkatesh
(Columbia) 
Closedstring mirror symmetry for subdomains
Abstract: We construct a symplectic cohomology theory for Liouville cobordisms that detects nontrivial elements of the Fukaya category. This theory is conjecturally mirror to the Jacobian ring of a LandauGinzburg superpotential on an affinoid subdomain. We illustrate this manifestation of mirror symmetry by examining cobordisms contained in negative line bundles. 
Date  Name  Title/Abstract 
013017  Yu Qiu, CUHK  Title: Spherical twists on 3CalabiYau categories of quivers with potentials from surfaces and spaces of stability conditions
Abstract: We study the 3CalabiYau category D(S) associated to a marked surface S. In the case when S is unpunctured, we show that the spherical twist group, which is a subgroup of autoequivalence group of D(S), is isomorphic to a subgroup of the mapping class group of S_Delta–the decorated version of S. In the case when S is an annulus, we prove that the space Stab of stability conditions on D(S) is contractible. We also present working progress on proving the simply connectedness of Stab for any unpunctured case and on studying Stab for the punctured case. 
020617 
Christoph Keller, Harvard School of Applied Science and Engineering 
Title: Mathieu Moonshine and Symmetry Surfing 
021317  Artan Sheshmani, Aarhus University/CMSA  Title: The theory of Nested Hilbert schemes on surfaces
Abstract: In joint work with Amin Gholampour and ShingTung Yau we construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of D\”{urrKabanovOkonek and the stable pair invariants of KoolThomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by CarlssonOkounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local DonaldsonThomas theory of threefolds that I will talk about, in talk 2. 
022017  Holiday — NO SEMINAR  
022717  Wenbin Yan, CMSA  Title: ArgyresDouglas Theories, Vertex Operator Algebras and Wild Hitchin Characters
Abstract: We discuss some interesting relations among 4d ArgylesDouglas (AD) theories, vertex operator algebras (VOA) and wild Hitchin system. We use the Coulomb branch index of AD theories to study geometric and topological data of moduli spaces of wild Hitchin system. These data show an one to one map between fixed points on the moduli space and irreducible modules of the VOA. Moreover, a limit of the Coulomb branch index of AD theories can be identified with matrix elements of the modular transform ST^kS in certain twodimensional VOAs. The appearance of VOAs, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising. 
030617  Tom Rudelius, Harvard University  Title: 6D SCFTs and Group Theory
Abstract: We will explore the surprising connection between certain classes of homomorphisms and certain classes of noncompact CalabiYau manifolds using 6D superconformal field theories as an intermediate link. 
031317  Spring Break — NO SEMINAR  
032017  Philippe Sosoe, CMSA  Title: New bounds for the chemical distance in 2D critical percolation
Abstract: We consider the problem of estimating the length, in lattice spacings, of the shortest open connection between the two vertical sides of a square of side length N in critical percolation, when N tends to infinity. This is known as the chemical distance between the sides. Kesten and Zhang asked if this length is asymptotically negligible compared to the length of the ”lowest crossing”, whose length can be expressed in terms of arm exponents and thus calculated quite precisely on the hexagonal lattice. With M. Damron and J. Hanson, we answered this question in 2015. In this talk, we present improved estimates on the chemical distance, using a new iteration technique. 
032717  Agnese Bissi, Harvard University  Title: Loops in AdS from conformal symmetry
Abstract: In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to nonplanar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, I’ll show how the polar part of the fourpoint, looplevel Mellin amplitudes can be fully reconstructed from the leadingorder data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the oneloop bubble diagram. I will end with a discussion on open problems and new developments. 
040317  Nathan Haouzi, University of California, Berkeley  Title: Little Strings and Classification of surface defects
Abstract: The socalled 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the sixdimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are Dbranes that wrap the 2cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the socalled BalaCarter labels that classify nilpotent orbits of these Lie algebras. 
041017  Burkhard Schwab, Harvard CMSA  Title: Large Gauge symmetries in Supergravity
Abstract: In the recent literature, a class of new symmetries — collectively known as “large gauge symmetries” — has emerged that governs the scattering of massless particles of very low energy on asymptotically flat space times. I will show that this statement extends to supergravity where an infinite family of fermionic symmetries can be derived. The algebra of these fermionic symmetries close in the BMS group and their Ward identity is the factorization of soft gravitinos in the Smatrix. 
041717  Ingmar Saberi, Universität Heidelberg  Title: Holographic lattice field theories
Abstract: Recent developments in tensor network models (which are, roughly speaking, quantum circuits designed to produce analogues of the ground state in a conformal field theory) have led to speculation that such networks provide a natural discretization of the AdS/CFT correspondence. This raises many questions: just to begin, is there any sort of dynamical model or lattice field theory underlying this connection? And how much of the usual AdS/CFT dictionary really makes sense in a discrete setting? I’ll describe some recent work that proposes a setting in which such questions can perhaps be addressed: a discrete spacetime whose bulk isometries nevertheless match its boundary conformal symmetries. Many of the first steps in the AdS/CFT dictionary carry over without much alteration to lattice field theories in this background, and one can even consider natural analogues of BTZ black hole geometries. 
042417  Patrick Jefferson, Harvard University  Title: Towards a classification of 5d N = 1 SCFTs
Abstract: I will discuss a new proposal for classifying fivedimensional SCFTs with N = 1 supersymmetry and a simple gauge algebra. This classification program entails studying supersymmetryprotected quantities on the Coulomb branch of moduli space using only representationtheoretic data, and subsumes all known predictions in the literature while predicting the existence of novel theories. Geometric constructions of 5d N = 1 theories via string compactifications interpret the supersymmetric protected data as geometric data associated to a local CalabiYau threefold, suggesting the possibility of translating this program into a partial cataloguing of CalabiYau geometries. 
050117  NO SEMINAR  
050817  NO SEMINAR  
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Date  Name  Title/Abstract 
091216  Chong Wang, Harvard  Title: A duality web in 2+1 dimensions
Abstract: I will discuss a web of field theory dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of these dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. Assuming some of these dualities, other dualities can be derived. I will present several consistency checks of the dualities and relate them to Sdualities in 3+1 dimensions. 
091916  Johannes Kleiner, University of Regensburg  Title: A New Candidate for a Unified Physical Theory
Abstract: The CFS theory is a new approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The goal of my talk is to explain the basic concepts and the general physical picture behind the approach. In particular, I will focus on the connection to contemporary physics. 
092616  Can Kozcaz, CMSA 
We explore a one parameter ζdeformation of the quantummechanical SineGordon and DoubleWell potentials which we call the Double SineGordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of ζ, the lowest ζ states turn out to be exactly solvable for DSG – a feature known as QuasiExactSolvability (QES) – and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instantonlike depen dence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits allorders perturbative states that are not normalizable, and hence, requires a nonperturbative energy shift. Both of these puzzles are solved by including complex saddles. 
100316 
Masahito Yamazaki, IMPU 
Title: Conformal Blocks and Verma Modules abstract: (for physicists) I will discuss analytic structures of the conformal block as a function of the scaling dimension. This will lead us torecursion relations for conformal blocks, which are also efficient for numerics. (for mathematicians) I will discuss representation theory of parabolic Verma modules for basic Lie superalgebras. In particular I will introduce a new determinant formula for the contravariant form. 
101716  Fabian Haiden, Harvard 
Title: “Balanced filtrations and asymptotics for semistable objects.” I will discuss some recent results which came out of the study of the flow on metrized quiver representations. This flow is a finitedimensional toy model for nonlinear heattype flows. In joint work with Katzarkov, Kontsevich, and Pantev, we find that the asymptotics of the flow on a given quiver representation define a filtration (indexed by R^\infty) which has a purely algebraic interpretation. A novel feature is the existence of nonlinear walls, on which asymptotics of the metric are described by nested logarithms. 
102416 
Arnav Tripathy, Harvard University 
Spinning BPS states and motivic DonaldsonThomas invariants I’ll describe a new chapter in the enumerative geometry of the K3 surface and its product with an elliptic curve in a long line of extensions starting from the classic YauZaslow formula for counts of rational nodal curves. In particular, I’ll give a stringtheoretic derivation of the threefold’s motivic DonaldsonThomas invariants given the Hodgeelliptic genus of the K3, a new quantity interpolating between the Hodge polynomial and the elliptic genus. 
103116 
Joseph Minahan, Uppsala University 
Supersymmetric gauge theories on $d$dimensional spheres Abstract: In this talk I discuss localizing super YangMills theories on spheres in various dimensions. Our results can be continued to noninteger dimensions, at least perturbatively, and can thus be used to regulate UV divergences. I will also show how this can provide a way to localize theories with less supersymmetry. 
110716 
SeungJoo Lee, Virginia Tech

Multiple Fibrations in CalabiYau Geometry and String Dualities Abstract: We study the ubiquity of multiple fibration structures in known constructions of CalabiYau manifolds and explore the role they play for string dualities. Upon introducing new tools for resolved CalabiYau varieties, we analyze a set of Ftheory effective theories associated to the different elliptic fibrations and relate them via the M/Ftheory correspondence. Explicit geometric examples will include higherrank MordellWeil groups and nonflat fibrations. In addition, in the context of heterotic/Ftheory duality, we also investigate the role played by multiple nested structures of K3 and elliptic fibrations in known and novel string dualities in various dimensions. 
111416 
Thomas Walpuski, MIT 
Title: Singular PHYM connections (on ACyl Kähler manifolds) Abstract: The celebrated Donaldson–Uhlenbeck–Yau Theorem asserts that a holomorphic vector bundle over a compact Kähler manifolds admits a projectively Hermitian Yang–Mills (PHYM) metric if and only if it is μ–polystable. Using a geometric regularization scheme, Bando–Siu extended the DUY Theorem to reflexive sheaves; however, they leave the singularities of the PHYM metrics unstudied. In the first part of this talk I will discuss a version of the DUY/BS Theorem for asymptotically cylindrical Kähler manifolds. I will briefly explain our motivation coming from G2 gauge theory and then sketch the crucial step of proof, which is how to use μ–stability at infinity to obtain a priori C^0 estimates. The second part of this talk focuses on understanding the singularities of PHYM metrics. In particular, I will explain a simple proof of uniqueness of tangent cones for singular projectively Hermitian Yang–Mills connections on reflexive sheaves at isolated singularities modelled on μ–polystable holomorphic bundles over \P^{n1}. This is joint work with A. Jacob and H. Sá Earp. 
112116 
Hee Cheol Kim, Harvard Physics 
Title: Defects and instantons in 5d SCFTs Abstract : In this talk I will discuss various BPS defects in 5d SUSY field theories. In the first part, I will talk about codimension 4 defects and their interaction with instanton particles. I will show that the partition function of this codimension 4 defect is related to Nekrasov’s qqcharacter. In the second part, I will talk about codimension 2 defects and instanton partition functions. I will also explain that the partition functions of the codimension 2 defects give rise to eigenfunctions of associated integral Hamiltonians. 
112816  NO MEETING THIS WEEK  
120516  Hansol Hong, CMSA 
Title: “Mirror construction via formal deformation of Lagrangians” Abstract: I’ll briefly review algebraic structures on categories that appear in homological mirror symmetry, and explain how the deformation of this algebraic structure on a Fukaya category can arise a mirror space. 
121216 