Previous Mathematical Physics seminars

Below is a list of Mathematical Physics Seminars held prior to the current academic year. For information on the current academic year’s seminars, please click here.

2018: 

Date……… Speaker…………. Title/Abstract
2-5-2018 Hyungchul Kim (Pohang University of Science and Technology) Seiberg duality and superconformal index in 3d

Abstract: I will discuss 3d N=2 supersymmetric gauge theories with a unitary gauge group and two matter fields in the adjoint representation. The low energy spectrum of BPS states of the theory can be studied from the superconformal index. The information on the low energy spectrum including monopole operators is essential to construct a Seiberg-type dual theory. Superconformal indices for a dual pair of the theories should be the same, which is a physical basis for a mathematical identity.

2-12-2018 Matthew Stroffregen

(MIT)

Equivariant Khovanov Spaces

Abstract: Associated to a link L in the three-sphere, Lipshitz-Sarkar constructed a topological space, well-defined up to stable homotopy, whose homology is the (even) Khovanov homology of L.  We extend this to construct an “odd Khovanov space” of L, whose homology recovers odd Khovanov homology. We also equip the odd Khovanov space with a natural involution whose fixed point set is the (even) Khovanov space of Lipshitz-Sarkar, and show that the even Khovanov space admits its own natural involution.  We outline some conjectures relating the even and odd Khovanov spaces. This is joint work with Sucharit Sarkar and Chris Scaduto.

2-26-2018 Jordan Keller

(Harvard)

Linear Stability of Schwarzschild Black Holes

Abstract: The Schwarzschild black holes comprise a static, spherically symmetric family of black hole solutions to the vacuum Einstein equations.  The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. We present results on the linear stability of the Schwarzschild black holes, joint work with Pei-Ken Hung and Mu-Tao Wang.

3-5-2018 Shinobu Hosono (Gakushuin University) Movable vs monodromy nilpotent cones of Calabi-Yau manifolds

abstract: I will show two interesting examples of mirror symmetry of Calabi-Yau complete intersections which have birational automorphisms of infinite order. I will first describe/observe mirror correspondences between the movable cones in birational geometry and the monodromy nilpotent cones which are defined at each boundary points (called LCSLs) in the moduli spaces and naturally glued together. In doing this, I will identify  “Picard-Lefschetzs monodromy transformations for flopping curves” in the mirror families. If time permits, I will show one more example of Calabi-Yau complete intersections for which we observe similar correspondence between the birational geometry and monodromy nilpotent cones. However, in this example, we observe that the correspondence becomes complete when we include a non-toric boundary point in the mirror family.

This is based on a recent paper with H. Takagi (arXiv:170

3-5-2018 Emanuel Scheidegger

(Albert Ludwigs University of Freiburg)

Periods and quasiperiods of modular forms and the mirror quintic at the conifold.

Abstract: We review the theory of periods of modular forms and extend it to quasiperiods. General motivic conjectures predict a relation between periods and quasiperiods of certain weight 4 Hecke eigenforms associated to hypergeometric one-parameter families of Calabi-Yau threefolds. We verify this prediction and discuss some of its implications.

3-19-2018

Room G02

Emanuel Scheidegger

(Albert Ludwigs University of Freiburg)

From Gauged Linear Sigma Models to Landau-Ginzburg orbifolds via central charge functions

Abstract: We review the categorical description of the Calabi-Yau/Landau-Ginzburg correspondence in terms of equivariant matrix factorizations in the gauged linear sigma model. We present the hemisphere partition function as a central charge function in the gauged linear sigma model. We study the relation of this function in the LG phase to the Chern character of equivariant matrix factorizations of the LG potential and generating functions of FJRW invariants.

3-26-2018 Yi Xie

SCGP

Surgery, Polygons and Instanton Floer homology

Abstract: Many classical numerical invariants (including Casson invariant, Alexander polynomial and Jones polynomial) for 3-manifolds or links satisfy surgery formulas relating three different 3-manifolds or links. All those invariants are categorified by certain Floer homologies (or Khovanov homology) which also satisfy so-called surgery exact triangles. In this talk I will discuss the notion of “surgery exact polygons” which appears in the SU(N)-instanton Floer homology theory. Roughly speaking, an “n-gon” is a relation among the Floer homology groups of 3-manifolds obtained by n different Dehn surgeries on a fixed knot. It generalizes the surgery exact triangle in SU(2)-instanton Floer homology. If time permits, I will also talk about a homological-mirror-symmetry-type  conjecture which motivates this work. This is joint work with Lucas Culler and Aliakbar Daemi.

4-2-2018 Cheuk-Yu Mak

Cambridge University

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.

4-9-2018

Room G02

Brandon B. Meredith

Embry-Riddle Aeronautical University

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.

4-16-2018 Yuan Gao

Stony Brook

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.

4-23-2018

Room G02

Baohua Fu

Chinese Academy of Science

Title: Equivariant compactifications of vector groups

Abstract: In 1954, Hirzebruch raised the problem to classify smooth compactifications of vector spaces with second Betti number 1, which is known till now up to dim 3. In 1999, Hassett-Tschinkel considered the equivariant version of this problem and obtained the classification up to dim. 3. I’ll report recent progress on this (equivariant) problem. In particular, we obtain the classification up to dimension 5.

4-30-2018 Dmitry Tonkonog

UC Berkeley

Title: Geometry of symplectic flux

Abstract: Symplectic flux measures the areas of cylinders swept in the process of an isotopy of a Lagrangian submanifold. This is a classical invariant which captures quantitative aspects of symplectic manifolds. I will report on joint work with Egor Shelukhin and Renato Vianna in which we study the geometry of flux using a technique inspired by mirror symmetry.

 

2017:

Date………. Name Title/Abstract
09-04-17 No Talk
09-11-2017 Yu-Shen Lin

(Harvad CMSA)

From the Decomposition of Picard-Lefschetz Transformation to Tropical Geometry

Abstract: Picard-Lefschetz 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 Picard-Lefschetz transformation into two elementary transformations from Floer theory. The idea will help to develop the tropical geometry for some hyperKahler surfaces.

09-18-17 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 non-unitary flat line bundles) do not vanish. This talk is based on joint work with Yunhyung Cho and Yong-Geun Oh.

09-27-17 Yu-Wei Fan

(Harvard)

Weil-Petersson geometry on the space of Bridgeland stability conditions

Abstract: Inspired by mirror symmetry, we define Weil-Petersson geometry on the space of Bridgeland stability conditions on a Calabi-Yau category. The goal is to further understand the stringy Kahler moduli space of Calabi-Yau manifolds.

This is a joint work with A. Kanazawa and S.-T. Yau.

10-04-17 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.

10-11-17 No Talk
10-18-2017 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 low-dimensional topology. In the second part, I’ll discuss the symplectic Torelli group for higher dimensional symplectic manifolds, and an ongoing project to use Gromov-Witten theory to detect interesting elements.

10-23-2017

*Monday*

Florian Beck

(Universität Hamburg)

Hitchin systems in terms of Calabi-Yau threefolds.

Abstract: Integrable systems are often constructed from geometric and/or Lie-theoretic data. Two important example classes are Hitchin systems and Calabi-Yau integrable systems. A Hitchin system is constructed from a compact Riemann surface  together with a complex Lie group with mild extra conditions. In contrast, Calabi-Yau integrable systems are constructed from a priori purely geometric data, namely certain families of Calabi-Yau threefolds.

Despite their different origins there is a non-trivial relation between Hitchin and Calabi-Yau integrable systems. More precisely, we will see in this talk that any Hitchin system for a simply-connected or adjoint simple complex Lie group is isomorphicto a Calabi-Yau integrable system (away from singular fibers).

11-01-2017

*12:30pm-1:30pm*

Chenglong Yu

(Harvard Math)

Picard-Fuchs systems of zero loci of vector bundle sections

Abstract: We propose an explicit construction for Picard-Fuchs 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.

11-06-2017

*Monday*

Pietro Benetti Genolini(Univ. of Oxford) Topological AdS/CFT

Abstract: I will describe a holographic dual to the Donaldson-Witten topological twist of gauge theories on a Riemannian four-manifold. Specifically, I will consider asymptotically locally hyperbolic solutions to Romans’ gauged supergravity in five dimensions with the four-manifold 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.

11-13-2017

*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 auto-equivalence. 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.

11-22-2017 No Talk
11-29-2017 Amitai Zernik

(IAS)

Computing the A∞ algebra of RP2m CP2m using open fixed-point 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 fixed-point 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 non-equivariant 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.

12-06-2017 Sarah Venkatesh

(Columbia)

Closed-string mirror symmetry for subdomains

Abstract: We construct a symplectic cohomology theory for Liouville cobordisms that detects non-trivial elements of the Fukaya category.  This theory is conjecturally mirror to the Jacobian ring of a Landau-Ginzburg superpotential on an affinoid subdomain.  We illustrate this manifestation of mirror symmetry by examining cobordisms contained in negative line bundles.

 

Date Name Title/Abstract
01-30-17 Yu Qiu, CUHKScreen Shot 2017-01-03 at 4.51.23 PM Title: Spherical twists on 3-Calabi-Yau categories of quivers with potentials from surfaces and spaces of stability conditions

Abstract: We study the 3-Calabi-Yau 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 auto-equivalence 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.

02-06-17

Christoph Keller, Harvard School of Applied Science and Engineering

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 Title: Mathieu Moonshine and Symmetry Surfing
02-13-17 Artan Sheshmani, Aarhus University/CMSA

Artan_Sheshmani_LK_828

Title: The theory of Nested Hilbert schemes on surfaces

Abstract: In joint work with Amin Gholampour and Shing-Tung 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\”{urr-Kabanov-Okonek and the stable pair invariants of Kool-Thomas. 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 Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local Donaldson-Thomas theory of threefolds that I will talk about, in talk 2.

02-20-17  Holiday — NO SEMINAR
02-27-17 Wenbin Yan, CMSA

wenbin yan

Title: Argyres-Douglas Theories, Vertex Operator Algebras and Wild Hitchin Characters

Abstract: We discuss some interesting relations among 4d Argyles-Douglas (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 two-dimensional VOAs. The appearance of VOAs, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

03-06-17 Tom Rudelius, Harvard UniversityTom Rudelius Title: 6D SCFTs and Group Theory

Abstract: We will explore the surprising connection between certain classes of homomorphisms and certain classes of non-compact Calabi-Yau manifolds using 6D superconformal field theories as an intermediate link.

03-13-17  Spring Break — NO SEMINAR
03-20-17 Philippe Sosoe, CMSA

sosoe

 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.

03-27-17 Agnese Bissi, Harvard University

Agnese Bissi

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 non-planar 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 four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order 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 one-loop bubble diagram. I will end with a discussion on open problems and new developments.

04-03-17 Nathan Haouzi, University of California, Berkeley Title: Little Strings and Classification of surface defects 

Abstract: The so-called 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 six-dimensional (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 D-branes that wrap the 2-cycles 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 so-called Bala-Carter labels that classify nilpotent orbits of these Lie algebras.

04-10-17 Burkhard Schwab, Harvard CMSA

bukharbSchwab

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 S-matrix.

04-17-17 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.

04-24-17 Patrick Jefferson, Harvard University Title:  Towards a classification of 5d N = 1 SCFTs

Abstract:  I will discuss a new proposal for classifying five-dimensional SCFTs with N = 1 supersymmetry and a simple gauge algebra. This classification program entails studying supersymmetry-protected quantities on the Coulomb branch of moduli space using only representation-theoretic 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 Calabi-Yau threefold, suggesting the possibility of translating this program into a partial cataloguing of Calabi-Yau geometries.

05-01-17  NO SEMINAR
05-08-17  NO SEMINAR
05-15-17
05-22-17
05-29-17

 

Date Name Title/Abstract
09-12-16 Chong Wang, Harvard

chong_125

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 S-dualities in 3+1 dimensions. 

09-19-16 Johannes Kleiner, University of Regensburg

Screen Shot 2016-08-30 at 11.58.35 AM

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.

09-26-16 Can Kozcaz, CMSA

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Cheshire Cat Resurgence

We explore a one parameter ζ-deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (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 Quasi-Exact-Solvability (QES) – and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like 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 all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles. 

10-03-16

Masahito Yamazaki, IMPU

11988

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.

10-17-16 Fabian Haiden, Harvard

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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 finite-dimensional toy model for non-linear heat-type 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 non-linear walls, on which asymptotics of the metric are described by nested logarithms.

 10-24-16

Arnav Tripathy, Harvard University

Arnav-photo-white-background

Spinning BPS states and motivic Donaldson-Thomas 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 Yau-Zaslow formula for counts of rational nodal curves. In particular, I’ll give a string-theoretic derivation of the threefold’s motivic Donaldson-Thomas invariants given the Hodge-elliptic genus of the K3, a new quantity interpolating between the Hodge polynomial and the elliptic genus.

10-31-16

Joseph Minahan, Uppsala University

438130_1joe

Supersymmetric gauge theories on $d$-dimensional spheres

Abstract:

In this talk I discuss localizing super Yang-Mills theories on spheres in various dimensions.  Our results can be continued to non-integer 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.

11-07-16

Seung-Joo Lee, Virginia Tech

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Multiple Fibrations in Calabi-Yau Geometry and String Dualities

Abstract:

We study the ubiquity of multiple fibration structures in known constructions of Calabi-Yau manifolds and explore the role they play for string dualities. Upon introducing new tools for resolved Calabi-Yau varieties, we analyze a set of F-theory effective theories associated to the different elliptic fibrations and relate them via the M-/F-theory correspondence. Explicit geometric examples will include higher-rank Mordell-Weil groups and non-flat fibrations. In addition, in the context of heterotic/F-theory 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.

11-14-16

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^{n-1}.

This is joint work with A. Jacob and H. Sá Earp.

11-21-16

Hee Cheol Kim, Harvard Physics

picture-23036-1380304599

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 co-dimension 4 defects and their interaction with instanton particles. I will show that the partition function of this co-dimension 4 defect is related to Nekrasov’s qq-character. In the second part, I will talk about co-dimension 2 defects and instanton partition functions. I will also explain that the partition functions of the co-dimension 2 defects give rise to eigenfunctions of associated integral Hamiltonians.

11-28-16 NO MEETING THIS WEEK
 12-05-16 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.

 12-12-16

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