Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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Abstract: Over the past decade we have witnessed the emergence of a plethora of correspondences between QFTs in various dimensions arising from higher dimensional SCFTs. In this talk I will overview another strategy (well-known to experts) to obtain correspondences building upon geometric engineering techniques. Several new applications and examples will be presented, involving supersymmetric theories in different dimensions. In particular, we will include … Read More

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Abstract: The Reshetikhin-Turaev construction for the quantum group U_q(gl(1|1)) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. Tangle Floer homology is a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. In earlier work with Ellis and Vertesi, we show that tangle … Read More

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Abstract: I will present a particular set of 4d N=2 SCFTs that can be labeled with a pair of Lie groups of type ADE. For specific choices, we get infinitely many theories arising from this construction that have their two central charges to be identical: a=c (without taking any large N limit). Interestingly, the Schur indices of these theories are … Read More

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Abstract: Mysterious duality was discovered by Iqbal, Neitzke, and Vafa in 2002 as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E_k. It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives … Read More

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Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on … Read More

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Abstract: Quantum field theories and string theories often lead to perturbative series which encode geometric information. In this lecture I will argue that, in the case of complex Chern-Simons theory, perturbative series secretly encode integer invariants, related in some cases to BPS counting. The framework which makes this relation possible is the theory of resurgence, where perturbative series lead to additional … Read More

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Abstract: 3d mirror symmetry predicts equivalences between topological twists of dual 3d N=4 theories, which we would like to understand as equivalences between their 2-categories of boundary conditions. Unfortunately, it is not known how to describe these 2-categories mathematically, although the B-side has been partially understood from work of Kapustin-Rozansky-Saulina and Arinkin. For abelian gauge theories, we propose that perverse … Read More

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Abstract: I will describe a physically-motivated conjectural approach (developed with Shamit Kachru and Arnav Tripathy) to the construction of hyperkahler deformations of $(\mathbb{R}^{4-r} \times T^r)/\Gamma$ with $0\le r \le 4$, where $\Gamma$ is a finite group, as well as recent work with Arnav Tripathy which proves some of these conjectures. This generalizes Kronheimer’s construction of ALE manifolds in the $r=0$ … Read More

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Abstract: \hat{Z} is a 3d TQFT whose existence was predicted by S. Gukov, D. Pei, P. Putrov, and C. Vafa in 2017 using 3d/3d correspondence. To each 3-manifold equipped with a spin^c structure, \hat{Z} is supposed to assign a q-series with integer coefficients that is categorifiable and provides an analytic continuation of Witten-Reshetikhin-Turaev invariants. In 2019, S. Gukov and C. Manolescu initiated … Read More