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DTSTART;TZID=America/New_York:20250220T100000
DTEND;TZID=America/New_York:20250220T110000
DTSTAMP:20260414T152944
CREATED:20250128T171842Z
LAST-MODIFIED:20250218T155455Z
UID:10003678-1740045600-1740049200@cmsa.fas.harvard.edu
SUMMARY:The geometry of pure spinor superfield formalism 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Simone Noja (Heidelberg University) \nTitle: The geometry of pure spinor superfield formalism \nAbstract: In this talk I will present a mathematical perspective on the pure spinor superfield formalism. In particular\, I will discuss how field multiplets in supersymmetric theories can be constructed mathematically from geometric data associated with certain algebraic varieties—namely\, the nilpotence variety of the (super)symmetry algebra of the theory. After discussing key examples\, I will\, time permitting\, outline a possible generalization of the formalism within the framework of derived geometry.
URL:https://cmsa.fas.harvard.edu/event/mathphys_22025/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-2.20.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250213T100000
DTEND;TZID=America/New_York:20250213T110000
DTSTAMP:20260414T152944
CREATED:20250128T171735Z
LAST-MODIFIED:20250212T182848Z
UID:10003677-1739440800-1739444400@cmsa.fas.harvard.edu
SUMMARY:The Structure of the Flux Landscape
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Damian Van de Heisteeg\, Harvard CMSA \nTitle: The Structure of the Flux Landscape \nAbstract: Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge\, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions\, emergent symmetries\, and the distribution of vacua. We demonstrate these ideas on an explicit example where we determine the landscape of exact flux vacua with a vanishing superpotential. We examine the implications of the tadpole bound\, which intriguingly confines flux vacua to real values of the moduli\, providing a potential avenue for addressing the strong CP problem. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_21325/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-2.13.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250206T100000
DTEND;TZID=America/New_York:20250206T110000
DTSTAMP:20260414T152944
CREATED:20241017T135403Z
LAST-MODIFIED:20250131T173042Z
UID:10003594-1738836000-1738839600@cmsa.fas.harvard.edu
SUMMARY:Quantum algebras and R-matrices from the equivariant affine Grassmannians
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Wenjun Niu\, Perimeter Institute \nTitle: Quantum algebras and R-matrices from the equivariant affine Grassmannians \nAbstract: In this talk\, I will explain my joint work with R. Abedin\, in which we construct\, for each Lie algebra g\, a Hopf algebra and a spectral R-matrix satisfying quantum Yang-Baxter equation. This Hopf algebra is a quantization of the Lie bi-algebra structure on T^*g[t] defined by Yang’s r-matrix\, and therefore we call it the Yangian of T^*g. The construction is based on the category of coherent sheaves on the equivariant affine Grassmannian associated to the formal group of g\, and is motivated by the study of the category of line defects in a 4 dimensional holomorphic-topological field theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_2625/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-2.6.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250130T100000
DTEND;TZID=America/New_York:20250130T110000
DTSTAMP:20260414T152944
CREATED:20250127T161217Z
LAST-MODIFIED:20250127T164602Z
UID:10003675-1738231200-1738234800@cmsa.fas.harvard.edu
SUMMARY:Stochastic Process and Noncommutative Geometry
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Zichang Wang (Tsinghua University) \nTitle: Stochastic Process and Noncommutative Geometry \nAbstract: We explain a stochastic approach to topological field theory and present a case study of quantum mechanical model and its relation to noncommutative geometry. For detail reference\, see https://arxiv.org/abs/2501.12360 \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_13025/
LOCATION:Hybrid
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-1.30.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241219T100000
DTEND;TZID=America/New_York:20241219T110000
DTSTAMP:20260414T152944
CREATED:20241203T214207Z
LAST-MODIFIED:20241219T193235Z
UID:10003600-1734602400-1734606000@cmsa.fas.harvard.edu
SUMMARY:Tyurin degenerations\, Relative Lagrangian foliations and categorification of DT invariants
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Artan Sheshmani (BIMSA) \nTitle: Tyurin degenerations\, Relative Lagrangian foliations and categorification of DT invariants \nAbstract: We discuss construction of a derived Lagrangian intersection theory of moduli spaces of perfect complexes\, with support on divisors on compact Calabi-Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We apply a Tyurin degeneration of the CY3 into a normal-crossing singular variety composed of Fano threefolds meeting along their anti-canonical divisor. We show that the moduli space over the Fano 4 fold given by total space of degeneration family satisfies a relative Lagrangian foliation structure which leads to realizing the moduli space as derived critical locus of a global (-1)-shifted potential function. We construct a flat Gauss-Manin connection to relate the periodic cyclic homology induced by matrix factorization category of such function to the derived Lagrangian intersection of the corresponding “Fano moduli spaces”. The later provides one with categorification of DT invariants over the special fiber (of degenerating family). The alternating sum of dimensions of the categorical DT invariants of the special fiber induces numerical DT invariants. If there is time\, we show how in terms of “non-derived” virtual intersection theory\, these numerical DT invariants relate to counts of D4-D2-D0 branes which are expected to have modularity property by the S-duality conjecture. This talk is based on joint work with Ludmil Katzarkov\, Maxim Kontsevich\, recent work with Jacob Krykzca\, and former work with Vladimir Baranovsky. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_121924/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-12.19.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241212T100000
DTEND;TZID=America/New_York:20241212T110000
DTSTAMP:20260414T152944
CREATED:20241209T191304Z
LAST-MODIFIED:20241219T193206Z
UID:10003601-1733997600-1734001200@cmsa.fas.harvard.edu
SUMMARY:The Quantum GIT conjecture
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Daniel Pomerleano (UMass Boston) \nTitle: The Quantum GIT conjecture \nAbstract: Let X be a Fano variety with G action. The quantum GIT conjecture predicts a formula for the quantum cohomology of “anti-canonical” GIT quotients X//G in terms of the equivariant quantum cohomology of X. The formula is motivated by ideas from 3- dimensional gauge theory (“Coulomb branches”) and provides a vast generalization of Batyrev’s formula for the quantum cohomology of a toric Fano variety. I will describe our ongoing work with C. Teleman proving this conjecture. Along the way\, I will also discuss integral versions of certain classical facts in the theory of Hamiltonian G-manifolds which are of independent interest. \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_121224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-12.12.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241121T103000
DTEND;TZID=America/New_York:20241121T113000
DTSTAMP:20260414T152944
CREATED:20240924T174856Z
LAST-MODIFIED:20241115T175402Z
UID:10003599-1732185000-1732188600@cmsa.fas.harvard.edu
SUMMARY:Skein valued curve counts for the topological vertex and knot conormals
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Tobias Ekholm\, Uppsala University \nTitle: Skein valued curve counts for the topological vertex and knot conormals \nAbstract: Combining the invariance of holomorphic curve counts in the skein module with a study of holomorphic curves at infinity of the vertex we find three simple skein operator polynomials that annihilates the (skein valued) topological vertex. We show that these operator polynomials together with natural initial conditions determine the partition function uniquely and then demonstrate that the original Aganagic-Klemm-Marino-Vafa formula for the topological vertex interpreted as a skein valued curve count satisfies the operator polynomials. This is joint work with Longhi and Shende. We end with a general discussion of similar ‘skein D-modules’ for knot conormals. \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_112124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241120T150000
DTEND;TZID=America/New_York:20241120T160000
DTSTAMP:20260414T152944
CREATED:20241010T135347Z
LAST-MODIFIED:20241115T183220Z
UID:10003593-1732114800-1732118400@cmsa.fas.harvard.edu
SUMMARY:A new construction of c = 1 conformal blocks
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Qianyu Hao\, University of Geneva \nTitle: A new construction of c = 1 conformal blocks\n\nAbstract: The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example\, when c = 1\, they are related to tau functions of Painlevé equations. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at c = 1 on C by using the “abelian” Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. This is based on a joint work with Andrew Neitzke.
URL:https://cmsa.fas.harvard.edu/event/mathphys_112024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.20.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241114T100000
DTEND;TZID=America/New_York:20241114T110000
DTSTAMP:20260414T152944
CREATED:20241107T191256Z
LAST-MODIFIED:20241112T151542Z
UID:10003598-1731578400-1731582000@cmsa.fas.harvard.edu
SUMMARY:(Un)likely intersections
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Tom Scanlon\, UC Berkeley \nTitle: (Un)likely intersections\n\nAbstract: The Zilber-Pink conjectures predicts that for an ambient special variety  (such as an abelian variety or a Shimura variety)\, if   is an irreducible algebraic subvariety which is not contained a proper special subvariety of  (e.g. a proper algebraic subgroup in the abelian variety case or a variety of Hodge type in the case of Shimura varieties)\, then the union of the unlikely intersections  as  ranges over the special subvarieties of  with  is not Zariski dense in .  While various instances of this conjecture have been proven\, it remains open in most cases of interest.  In this lecture\, I will describe some of my work with Jonathan Pila in which we prove an effective function field version of this conjecture along with a counterpart to the Zilber-Pink conjecture proven with Sebastian Eterović:  after accounting for some geometric obstructions\, the likely intersections\, i.e. the union of the intersections  with  special and \,  are dense in the Euclidean topology in .   Our techniques for both results come from o-minimal complex analysis and differential algebra.\n\n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_111424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.14.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241107T100000
DTEND;TZID=America/New_York:20241107T110000
DTSTAMP:20260414T152944
CREATED:20241104T150020Z
LAST-MODIFIED:20241104T171029Z
UID:10003597-1730973600-1730977200@cmsa.fas.harvard.edu
SUMMARY:Bounds and Dualities of Type II Little String Theories
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Fabian Ruehle (Northeastern University) \nTitle: Bounds and Dualities of Type II Little String Theories \nAbstract: The goal of this seminar is to introduce Type II Little String Theories (LSTs)\, which are six-dimensional supersymmetric QFTs. We explore how to geometrically engineer these theories within the context of M-/F-theory (top-down) as well as consistent QFT realizations (bottom-up). After that\, we turn to the worldsheet theory of LSTs\, which are two-dimensional N=(0\,4) SCFTs. Using anomaly inflow and unitarity\, we derive strong constraints on the rank of their global symmetry algebras.
URL:https://cmsa.fas.harvard.edu/event/mathphys_11724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.7.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241031T100000
DTEND;TZID=America/New_York:20241031T110000
DTSTAMP:20260414T152944
CREATED:20241022T175333Z
LAST-MODIFIED:20241022T180010Z
UID:10003596-1730368800-1730372400@cmsa.fas.harvard.edu
SUMMARY:Mirror Construction for Nakajima Quiver Varieties
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Ju Tan (Boston University) \nTitle: Mirror Construction for Nakajima Quiver Varieties \nAbstract: Quiver possesses a rich representation theory. On the one hand\, it exhibits a deep connection with instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand\, quivers also capture the formal deformation space of a Lagrangian submanifold. In this talk\, we will discuss these relations more explicitly from the perspective of SYZ mirror symmetry. In particular\, we will introduce the notion of framed Lagrangian immersions\, the Maurer-Cartan deformation spaces of which are Nakajima quiver varieties/ stacks. Besides\, we will realize the ADHM construction as a mirror symmetry phenomenon. This is based on the joint work with Jiawei Hu and Siu-Cheong Lau. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_103124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.31.2024.docx.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241024T100000
DTEND;TZID=America/New_York:20241024T110000
DTSTAMP:20260414T152944
CREATED:20241018T143428Z
LAST-MODIFIED:20241018T144254Z
UID:10003595-1729764000-1729767600@cmsa.fas.harvard.edu
SUMMARY:Heterotic Little String Theories and Inequivalent Genus-One Fibrations
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Hamza Ahmed\, Northeastern University \nTitle: Heterotic Little String Theories and Inequivalent Genus-One Fibrations \nAbstract: Little String Theories (LSTs) are 6D Supersymmetric quantum field theories (SQFTs) with an additional physical relation called T-duality. This enables us to arrange them into equivalence classes\, where each equivalence class has 6D LSTs that lead to the same 5D effective theory when compactified on a circle. The problem of finding T-dual LSTs can be mapped to the problem of finding inequivalent genus-one fibrations of the same non-compact Calabi-Yau (CY) threefold. For T-dual theories\, certain field theory data is expected to match\, which then implies certain invariants of inequivalent fibrations. Focusing on theories with 8 supercharges (Heterotic LSTs)\, we use this geometry-field theory equivalence to study the T-duality landscape\, particularly in the case where the genus-one fiber does not have a section\, leading to what are called twisted T-dual theories. Based on the excellent agreement we find between the geometry and field theory arguments\, we conjecture the existence of a new class of twisted T-duals for which no geometric construction is known. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_102424/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.24.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241003T100000
DTEND;TZID=America/New_York:20241003T110000
DTSTAMP:20260414T152944
CREATED:20240927T144416Z
LAST-MODIFIED:20240927T183006Z
UID:10003592-1727949600-1727953200@cmsa.fas.harvard.edu
SUMMARY:Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Chuck Doran\, Harvard CMSA \nTitle: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds \nAbstract: Smooth $M_m$-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in terms of the choice of a generalized functional invariant and\, in the case $m=1$\, a generalized homological invariant. The resulting geometries generally exhibit a small number of complex structure moduli greater or equal to two. A concrete choice of these invariants realizes (almost all of) the known Calabi-Yau geometries with exactly two moduli and allows us to describe completely the structure of the corresponding moduli spaces. The corresponding variations of Hodge structure are entirely determined by the regular periods\, for which we obtain a generic expression in terms of $m$ and three integers $i\,j\,s$. Using the form of this period and Batyrev-Borisov mirror symmetry we explicitly construct the corresponding mirror CY 3-folds with two Kaehler moduli and show consistency with the DHT conjecture. In the cases with $s=0$\, the mirror CY 3-folds are again K3-fibered but with the mirror $<2m>$-polarization. The generic form of the periods allows us to derive generic modular expressions for the A-model topological string free energies and we argue that those are a consequence of a Tyurin degeneration of the generalized functional invariant with the central fiber being an $M_m$-polarized K3. This is joint work with Boris Pioline and Thorsten Schimannek.
URL:https://cmsa.fas.harvard.edu/event/mathphys_10324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.3.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240926T100000
DTEND;TZID=America/New_York:20240926T110000
DTSTAMP:20260414T152944
CREATED:20240917T135417Z
LAST-MODIFIED:20240920T143613Z
UID:10003508-1727344800-1727348400@cmsa.fas.harvard.edu
SUMMARY:Witten deformation for non-Morse functions and gluing formulas 
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Junrong Yan (Northeastern University) \nTitle: Witten deformation for non-Morse functions and gluing formulas \nAbstract: Witten deformation is a versatile tool with numerous applications in mathematical physics and geometry. In this talk\, we will focus on the analysis of Witten deformation for a family of non-Morse functions\, which leads to a new technique for studying the gluing formulas of global spectral invariants (such as eta invariants\, analytic torsions\, and some invariants related to Feynman diagrams\, etc.). We will then discuss some applications of this new method. \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_92624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-09.26.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240919T100000
DTEND;TZID=America/New_York:20240919T110000
DTSTAMP:20260414T152944
CREATED:20240917T135258Z
LAST-MODIFIED:20240917T155533Z
UID:10003507-1726740000-1726743600@cmsa.fas.harvard.edu
SUMMARY:Feynman graph integrals from topological holomorphic theories 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Minghao Wang (Boston University) \nTitle: Feynman graph integrals from topological holomorphic theories \nAbstract: Feynman graph integrals from topological theories were developed by M. Kontsevich\, S. Axelrod and I. M. Singer in 1990s. These integrals have many mathematical applications\, such as knot invariants\, operad theory and formality theorems. In this talk\, I will talk about Feynman graph integrals from topological-holomorphic theories. In particular\, I will prove the finiteness of Feynman graph integrals when spacetime is flat spaces and a vanishing result of graph integrals. Combining the vanishing result with Batalin-Vilkovisky(BV) formalism\, we can show the absence of anomalies of topological-holomorphic theories on flat spaces with at least two topological dimensions. As a consequence\, we can construct factorization algebras of quantum observables. This is a joint with Brian Williams.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-09.19.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T100000
DTEND;TZID=America/New_York:20240912T110000
DTSTAMP:20260414T152944
CREATED:20240907T170232Z
LAST-MODIFIED:20240917T140551Z
UID:10003412-1726135200-1726138800@cmsa.fas.harvard.edu
SUMMARY:Twisted Tools for (Untwisted) Quantum Field Theory
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Justin Kulp (Simons Center for Geometry and Physics) \nTitle: Twisted Tools for (Untwisted) Quantum Field Theory \nAbstract: One of the most important properties of QFTs is that they can be deformed by “turning on interactions.” Essentially every observable can be viewed as coupling the theory to some external system. Famously\, adding interactions (generically) breaks scale invariance\, leading to familiar ideas of EFTs and RG flows in the space of QFTs. An underappreciated fact is that one can actually consider flows generated by any transformation\, not just the usual scale transformations. \nIn my talk\, I will discuss a flow in the space of QFTs coming from (an analogue of) BRST symmetry. The beta-function for this “BRST-flow” controls deformations of the QFT and is highly mathematically constrained\, endowing the space of interactions with an L∞ algebra structure. The structure constants/brackets of the L∞ algebra are highly computable (requiring only a first course in QFT to compute) and contain familiar information such as anomalies and Operator Product Expansion coefficients. I will prove a non-renormalization theorem for holomorphic-topological QFTs with more than one topological direction\, which can be thought of as a generalization of a formality theorem of Kontsevich. Time permitting\, I will discuss how this formalism enables the systematic computation of minimal BPS operators in supersymmetric QFTs and describe the “holomorphic confinement” of N=1 SYM.  Based on arXiv:2403.13049.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
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DTSTART;TZID=America/New_York:20240624T080000
DTEND;TZID=America/New_York:20240626T170000
DTSTAMP:20260414T152944
CREATED:20240415T161428Z
LAST-MODIFIED:20241212T160959Z
UID:10003355-1719216000-1719421200@cmsa.fas.harvard.edu
SUMMARY:Workshop on Fibration and Degeneration in Calabi-Yau Geometry
DESCRIPTION:Workshop on Fibration and Degeneration in Calabi-Yau Geometry \nDates: June 24-26\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nOrganizer: Chuck Doran\, Harvard CMSA \n\nCalabi-Yau manifolds occupy a central place in geometry. Their critical role as the cut-case between basic Fano building blocks and the zoo of General Type manifolds is key to the wide variety of important applications of Calabi-Yau geometry to theoretical physics. In turn\, ideas from theoretical physics\, such as Mirror Symmetry\, help shape investigations in Calabi-Yau geometry \nThis workshop focuses on a structural feature of Calabi-Yau geometry identified a decade ago by Doran\, Harder\, and Thompson. It is an organizing principle that conjecturally underlies any and all constructions of mirror pairs of Calabi-Yau manifolds. Put simply\, the DHT Mirror Symmetry slogan is: “Degeneration is mirror to fibration.” \n\n\nConfirmed Speakers: \n\nDavid Favero (University of Minnesota)\nAndrew Harder (Lehigh University)\nJesse Huang (University of Alberta)\nMohsen Karkheiran* (University of Alberta)\nMatt Kerr* (Washington University in St. Louis)\nThorsten Schimannek* (Utrecht University)\nMichael Schultz (Virginia Tech)\nAlan Thompson (Loughborough University)\nFenglong You (University of Nottingham & ETH Zurich)\n\n*= via Zoom \n  \nSchedule \nMonday\, June 24\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Alan Thompson\, Loughborough University\nTitle: Mirror symmetry for fibrations and degenerations of K3 surfaces\nAbstract: I will describe recent progress\, joint with Luca Giovenzana\, on the DHT problem for K3 surfaces. I will give an lattice-theoretic definition for when a Tyurin degeneration of K3 surfaces and an elliptically-fibred K3 surface\, with an appropriate splitting of the base\, form a mirror pair. I will then explain how this definition is compatible with lattice polarised mirror symmetry for K3 surfaces and with Fano-LG mirror symmetry for (quasi) del Pezzo surfaces. The upshot will be a concrete statement of the DHT conjecture for K3 surfaces. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: David Favero\, University of Minnesota\nTitle: Homotopy Path Algebras and Resolutions\nAbstract: A homotopy path algebra is like a directed version of the group ring on a fundamental group.  One can imagine a directed graph (quiver) embedded in a topological space and considering the path algebra up to homotopy.  Alternatively\, one can think of homotopy classes of directed paths in a stratified topological space.  I will introduce homotopy path algebras and describe their connections to mirror symmetry and resolutions of coherent sheaves on toric varieties. \n3:00 – 4:00 pm\nSpeaker: Andrew Harder\, Lehigh University\nTitle: Tropical Hodge theory for hypersurfaces and Clarke duality\nAbstract: Results of Itenberg\, Katzarkov\, Mikhalkin\, and Zharkov (IKMZ) show that if a projective variety admits a smooth tropicalization\, then there is a collection of sheaves on its tropicalization that can be used to compute its Hodge numbers. However\, smooth tropicalizations fail to exist even in the case of toric hypersurfaces. In work with Sukjoo Lee\, we show that for any toric hypersurface\, an analogue of IKMZ’s result holds. I’ll discuss this sheaf\, and how this allows us to prove that Clarke dual pairs of Landau-Ginzburg models satisfy a particular Hodge number duality. This is a vast generalization of work of Batyrev and Borisov from the 90s. \n4:00 – 4:30 pm: Coffee/Tea \n  \nTuesday\, June 25\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Matt Kerr\, Washington University in St. Louis\nTitle: Hypergeometric families and Beilinson’s conjectures\nAbstract: I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions. These are analogous to elements of the Mordell-Weil group for families of elliptic curves\, and produce solutions to certain inhomogeneous Picard-Fuchs equations. This is part of a joint project with Vasily Golyshev in which we numerically verify Beilinson’s conjectures in some new cases. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: Fenglong You\, University of Nottingham & ETH Zurich\nTitle: Theta functions in mirror symmetry\nAbstract: To obtain a mirror of a Calabi—Yau manifold using Gross—Siebert’s intrinsic mirror symmetry\, one considers a maximally unipotent monodromy degeneration of the Calabi—Yau and take proj of the degree zero part of a relative quantum cohomology ring associated with the degeneration. Theta functions form a canonical basis of the degree zero part of the relative quantum cohomology ring. Theta functions can also be defined in terms of punctured invariants of the broken line type. I will explain a variant of intrinsic mirror symmetry using orbifold invariants\, theta functions for general snc pairs and a relation with the DHT conjecture. \n3:00 – 4:00 pm\nSpeaker: Mohsen Karkheiran\, University of Alberta\nTitle: Emergence of Heterotic-Type II duality from DHT conjecture\nAbstract: The duality between Heterotic and Type IIA strings was conjectured in mid-90’s based on the properties of 4D N=2 field theories and solitonic strings in 6D. Here\, we show that this duality can also emerge from the DHT conjecture. We assume both IIA and IIB strings are compactified over toric Calabi-Yau threefolds which admit K3-fibrations with arbitrary polarizations. Then by applying the Hori-Vafa mirror symmetry to the “pieces” of these Calabi-Yau manifolds\, we will be able to derive the defining data for Heterotic strings. This approach works for any gauge group on the Heterotic side\, and we will show how it can be practically useful to derive the Heterotic dual for any toric Calabi-Yau threefolds in Type IIA or F-theory. \n4:00 – 4:30 pm: Coffee/Tea \n  \nWednesday\, June 26\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Thorsten Schimannek\, Utrecht University\nTitle: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds\nAbstract: Smooth M_m-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in [DHNT] and [KT] in terms of the choice of a generalized functional invariant (GFI) and\, in the case m=1\, a generalized homological invariant (GHI). The resulting geometries generally exhibit a small number of complex structure moduli greater or equal to two. I will start my talk by discussing a concrete choice of these invariants that realizes (almost all of) the geometries with exactly two moduli and describe the structure of the corresponding moduli spaces. The corresponding variations of Hodge structure are entirely determined by the regular periods\, for which we obtain a generic expression in terms of m and three integers i\,j\,s. Using the form of this period and Batyrev-Borisov mirror symmetry I will then explicitly construct the corresponding mirror CY 3-folds with two Kaehler moduli and show consistency with the DHT conjecture. In the cases with s=0\, the mirror CY 3-folds are again K3-fibered but with a 2m-polarization. The generic form of the periods allows us to derive generic modular expressions for the A-model topological string free energies and we argue that those are a consequence of a Tyurin degeneration of the GFI with the central fiber being an M_m-polarized K3.\nThe talk is based on work in progress with Charles Doran and Boris Pioline. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: Michael Schultz\, Virginia Tech\nTitle: Mirror Symmetry from Irrationality Proofs and a Proposal for Local Invariants\nAbstract: While Apéry’s original proof of the irrationality of ζ(3) stunned the mathematics community in 1978\, subsequent generations of mathematicians (including a number of those at this workshop) have discovered geometric and modular structures underlying these irrationality proofs that are arguably even more striking. One such well known example are connections to modular pencils of elliptic curves and K3 surfaces and their Picard-Fuchs operators\, which exhibit maximally unipotent monodromy. These objects are respectively mirror dual to anticanonical divisors in certain del Pezzo surfaces and Fano threefolds\, and their Picard-Fuchs operators to the A-side connection on small quantum cohomology for these varieties. Although the Yukawa couplings calculated in classical mirror symmetry for elliptic curves and K3 surfaces are trivial\, I will show in this talk how a blend of the perspectives above allows one to define “virtual” Yukawa couplings for these families that are not trivial. It will be proposed that the utility of this perspective is in computing local invariants related to the mirror\, which recovers some known results in the literature and utilizes connections to work on the DHT conjecture and the twist construction of Doran & Malmendier. \n3:00 – 4:00 pm\nSpeaker: Jesse Huang\, University of Alberta\nTitle: An invitation to global toric mirror symmetry \n4:00 – 4:30 pm: Coffee/Tea \n  \n \n\n 
URL:https://cmsa.fas.harvard.edu/event/fibration/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Workshop
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