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Quantum Field Theory and Physical Mathematics Seminar Speaker: Minghao Wang, Boston University Title: Graph integrals on Kahler manifolds Abstract: I will talk about my recent work with Junrong Yan. We proved the convergence of Graph integrals on analytic Kahler manifolds in the sense of Cauchy principal values, which are originally from holomorphic quantum field theories. […] |
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Geometry and Quantum Theory Seminar Speaker 1: Max Hubner, CMSA Title: On Topological Structures in String Theory Abstract: Geometric engineering constructions in string theory often realize QFTs relative to an extra-dimensional geometry. This perspective parallels the symmetry TFT construction where a QFT is presented relative to its extra-dimensional symmetry quiche. Unsurprisingly, as we will discuss, […] |
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https://youtu.be/0FCgpyCfb4o New Technologies in Mathematics Seminar Speaker: Michael Borinsky, Perimeter Institute Title: Tropicalized quantum field theory Abstract: Quantum field theory (QFT) is one of the most accurate methods for making phenomenological predictions in physics, but it has a significant drawback: obtaining concrete predictions from it is computationally very demanding. The standard perturbative approach expands an […] |
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Differential Geometry and Physics Seminar Speaker: Valentino Tosatti, NYU Courant Institute Title: Special Kähler geometry and collapsing Abstract: Special Kähler geometry was first discovered in the context of N=2 supersymmetric 4D gauge theories, and it also plays a prominent role in mirror symmetry. A key observation of Donagi-Witten and Freed is that the base of every algebraic integrable system […] |
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Member Seminar Speaker: Saman Habibi Esfahani Title: Local Donaldson-Scaduto conjecture Abstract: This talk is based on joint works with Gora Bera and Yang Li. Motivated by collapsing Calabi-Yau 3-folds and G2-manifolds with Lefschetz K3 fibrations in the adiabatic setting, Donaldson and Scaduto conjectured the existence and uniqueness of a special Lagrangian pair-of-pants in the Calabi-Yau […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Kevin Costello (Perimeter Institute) Title: Non-perturbative aspects of self-dual gauge theory Abstract: Self-dual gauge theory is conformal in perturbation theory, but has a non-trivial beta-function when instanton effects are included. I will give two computations of this beta-function, one based on the Grothendieck-Riemann-Roch formula and one using holography […]
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Colloquium Speaker: Alexei Borodin, MIT Title: Geometry of dimer models Abstract: Random dimer coverings of large planar graphs are known to exhibit unusual and visually apparent asymptotic phenomena that include formation of frozen regions and various phases in the unfrozen ones. For a specific family of subgraphs of the (periodically weighted) square lattice known as the Aztec diamonds, the asymptotic behavior of dimers admits a precise description in […] |
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Geometry and Quantum Theory Seminar Speakers: Daniel Spiegel, Harvard Math Title: A Classifying Space for Phases of Matrix Product States Abstract: Alexei Kitaev has conjectured that there should be a loop spectrum consisting of spaces of gapped invertible quantum spin systems, indexed by spatial dimension d of the lattice. Motivated by Kitaev’s conjecture, I will […] |
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https://youtu.be/04E8r76TetQ New Technologies in Mathematics Seminar Speaker: Alex Damian, Harvard Title: Understanding Optimization in Deep Learning with Central Flows Abstract: Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of […] |
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Algebra Seminar Speaker: David Treumann (Boston College) Title: Profinite tensor powers Abstract: I'll discuss the problem of defining a tensor product of profinitely many copies of a vector space V, and propose a definition $\bigotimes_X^{mcc} V$ in the special situation that (1) V is finite-dimensional over F_2, and (2) the profinite X indexing the tensor […]
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https://youtu.be/vf3pIK9I9HI Differential Geometry and Physics Seminar Speaker: Xingyang Yu, Virginia Tech Title: Symmetries and Moduli Spaces: Baby Steps beyond Calabi-Yau Abstract: I will explore the interplay between symmetries and moduli spaces in string compactifications, starting from the familiar Calabi–Yau case and then taking some baby steps toward more general settings. A classical benchmark is the line […] |
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Member Seminar Speaker: Lorenzo Riva Title: The Rozansky-Witten field theory in the functorial TQFT formalism Abstract: This will be a broad talk about the topic of my PhD thesis. We will discuss a particular example of a 3D field theory from physics called Rozansky-Witten which is interesting from both a physical and a mathematical point […] |
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Geometry and Quantum Theory Seminar Speaker: Dylan Galt, Harvard (60 minute talk) Title: What is a "nonlinear" near-symplectic form? Abstract: In this talk, I will explain how one might understand this question and why a possible answer can be found in the geometry of coassociative 4-folds, a special class of minimal submanifolds discovered by Harvey and Lawson. […] |
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Algebra Seminar Speaker: Linquan Ma (Purdue University) Title: Lech's inequality and stability of local rings Abstract: We explore Lech's inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech's inequality and show its connections with singularities of asymptotically semistable varieties […]
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Differential Geometry and Physics Seminar Speaker: Andy Neitzke, Yale Title: Abelianization of tau functions Abstract: The symplectic and hyperkahler geometry of moduli spaces of flat connections over Riemann surfaces is in a sense quantized by the theory of isomonodromic tau functions. These functions in turn arise as partition functions in the conformal field theory of […] |
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Member Seminar Speaker: Blake Bordelon Title: DMFT, Two Point Correlations of Resolvents, and Applications to Machine Learning Theory Abstract: Machine learning algorithms evolve the parameters of a model in a high dimensional and disordered loss landscape. To characterize the effects of random initialization of model parameters, randomly sampled training data, and the effect of SGD noise, it […]
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Freedman Seminar Speaker: Michael Freedman, Harvard CMSA Title: Sullivan's work on Lipschitz structures Abstract: I'll begin with an elementary, but now little known, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I'll explain Dennis Sullivan's enhancement of Kirby's torus trick (which relies […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Adrian López-Raven, Perimeter Title: Categorical 't Hooft expansion and Chiral Algebras Abstract: In https://arxiv.org/abs/2411.00760, we show how holographic dual B-model backgrounds can be systematically derived from the 't Hooft expansion of specific families of chiral algebras. The resulting holographic dual backgrounds are typically non-commutative and appear to be […] |
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CMSA Q&A Seminar Speaker: Thomas Grimm, Utrecht & CMSA Topic: What is o-minimality and what is it good for?
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New Technologies in Mathematics Seminar Speaker: María Inés de Frutos Fernández, Mathematical Institute, University of Bonn Title: The Carleson project: A collaborative formalization Abstract: A well-known result in Fourier analysis establishes that the partial Fourier sums of a smooth periodic function $f$ converge uniformly to $f$, but the situation is a lot more subtle for […] |
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Algebra Seminar Speaker: Zhiwei Yun, MIT Title: Character sheaves on the loop Lie algebra and its global implications Abstract: Motivated by Lusztig's definition of character sheaves on a reductive Lie algebra, we propose a definition of character sheaves on the loop Lie algebra. The construction can be viewed as a p-adic analogue of the orbit […]
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Differential Geometry and Physics Seminar Speaker: Ron Donagi, UPenn Title: On some new irrationality results Abstract: An algebraic variety X is rational if a Zariski-open subset of X is isomorphic to a Zariski-open subset of projective space. A weaker property is unirationality: X is unirational if a Zariski-open subset of projective space maps onto a Zariski-open […] |
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Member Seminar Speaker: Stephen Landsittel, CMSA Title: Analytic Spread of Binomial Edge Ideals Abstract: To an ideal J in a polynomial ring R over a field K we associate its analytic spread \ell(J), which is the dimension of the fiber cone F(J) of J. When J is graded and generated in a single degree d, then […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Grigorii Taroian, U Toronto Title: de Rham Theory in Derived Differential Geometry Abstract: In the talk, I will describe recent progress in building a version of de Rham theory for derived manifolds and derived differentiable stacks. Derived differential geometry is a nascent field applying techniques from derived algebraic […]
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Colloquium Speaker: Eran Nevo (Hebrew University of Jerusalem) Title: Rigidity, expansion and polytopes Abstract: Given a graph G and an embedding of its vertices in R^d, what continuous motions of the vertices preserve all edge lengths? Clearly all motions induced by an isometry of R^d do, these are the trivial motions; are there any others? If the answer […] |
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Geometry and Quantum Theory Seminar Speakers: (1) Elliott Gesteau, CMSA (60 min) and (2) Sanjay Raman, Harvard (30 min) (1) Title: Holography for closed universes Abstract: Recent advances in holography and black hole physics have prompted a number of new puzzles related to the physics of closed universes, which can be argued to have a one-dimensional […] |
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Algebra Seminar Speaker: Roman Bezrukavnikov, MIT Title: Affine Springer fibers and representations Abstract: Relating representation categories of interest, such of modules over the quantum group, to topology of loop spaces has been an important theme in representation theory for some decades. I will describe a result of this sort involving a geometric object that has […]
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Differential Geometry and Physics Seminar Speaker: Jian Song, Rutgers University Title: RCD structures on singular Kahler varieties Abstract: Let X be a 3-dimensional projective variety with klt singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature bounded below induces a unique compact RCD space homeomorphic to the projective […] |
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Member Seminar Speaker: Sunghyuk Park, CMSA Title: Skein remain the same Abstract: The count of holomorphic curves in a Calabi-Yau 3-fold ending on a Lagrangian is famously not deformation invariant, but Ekholm and Shende have shown that it can be made invariant by counting in the skein. Given a 3-manifold M and a branched cover arising from […] |
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