There are no events at the Simons Center today. Here are the events for this week
Monday, March 23rd, 2026
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Daniel Pomerleano - Frobenius intertwiners and the p-adic Gamma class
Time: 12:30 PM - 1:55 PM
Location: Math P-131
Speaker: Daniel Pomerleano
Abstract: In recent joint work with Bai, Lee, and Seidel, we formulated a conjecture regarding the existence of an Frobenius structure on the quantum cohomology of Fano and Calabi-Yau manifolds. This candidate structure is constructed from Dwork’s p-adic Gamma function, and its conjectural integrality properties are linked to properties of Givental’s fundamental solution. In this talk, I will describe proofs of this conjecture for certain Fanos and Calabi-Yau 3-folds as well as connections to an algebro-geometric formula of Katz for p-curvature.
Speaker: Daniel Pomerleano
Abstract: In recent joint work with Bai, Lee, and Seidel, we formulated a conjecture regarding the existence of an Frobenius structure on the quantum cohomology of Fano and Calabi-Yau manifolds. This candidate structure is constructed from Dwork’s p-adic Gamma function, and its conjectural integrality properties are linked to properties of Givental’s fundamental solution. In this talk, I will describe proofs of this conjecture for certain Fanos and Calabi-Yau 3-folds as well as connections to an algebro-geometric formula of Katz for p-curvature.
Tuesday, March 24th, 2026
Math Event: Geometry/Topology Seminar: No seminar this week: Della Pietra lecture
Time: 4:00 PM - 5:15 PM
Location: P-131
Della Pietra General Public Lecture by Persi Diaconis (Stanford)
Time: 4:30 PM - 5:30 PM
Location: Della Pietra Family Auditorium, room 103
Title: Â UNDERSTANDING COINCIDENCES
Abstract: Coincidences astound us. They can affect where we live (and with whom), work and all sorts of things. I will review ideas of Freud and Jung on the psychology of coincidences. I will also show that sometimes, a bit of thought shows 'it's not so surprising after all'. A small set of tools and examples lead to a checklist and ways of quantifying things. This is a math talk, but aimed at a very general audience.
Title: Â UNDERSTANDING COINCIDENCES
Abstract: Coincidences astound us. They can affect where we live (and with whom), work and all sorts of things. I will review ideas of Freud and Jung on the psychology of coincidences. I will also show that sometimes, a bit of thought shows 'it's not so surprising after all'. A small set of tools and examples lead to a checklist and ways of quantifying things. This is a math talk, but aimed at a very general audience.
Wednesday, March 25th, 2026
Della Pietra High School Lecture by Persi Diaconis (Stanford)
Time: 11:00 AM - 12:00 PM
Location: 103
Title: THE SEARCH FOR RANDOMNESS
Abstract: I will review some of our most primitive notions of random phenomena; flipping a coin, shuffling cards and throwing a dart at the wall. Thinking about things, we can show that usually we are lazy and things are not at all random. Physics and mathematics and just plain common sense come in. This is a math talk aimed at an undergraduate audience--it has lots of stories (and you can also go make money in a casino).
Title: THE SEARCH FOR RANDOMNESS
Abstract: I will review some of our most primitive notions of random phenomena; flipping a coin, shuffling cards and throwing a dart at the wall. Thinking about things, we can show that usually we are lazy and things are not at all random. Physics and mathematics and just plain common sense come in. This is a math talk aimed at an undergraduate audience--it has lots of stories (and you can also go make money in a casino).
YITP Event: Kai Chung (Rice University) -- "Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chain"
Time: 11:00 AM - 12:00 PM
Location:
Title: /b> Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit ChainÂ
Abstract: /b> Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group G (reducing to ordinary qubits when G=ℤ2). We construct Ising-type transverse-field Hamiltonians with Rep(G) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group G. For non-Abelian G, the symmetry is non-invertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain -- features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with non-trivial internal Hilbert spaces and fusion rules. Our work identifies properties of non-invertible symmetry breaking that existing quantum hardware can probe.
Title: /b> Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit ChainÂ
Abstract: /b> Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group G (reducing to ordinary qubits when G=ℤ2). We construct Ising-type transverse-field Hamiltonians with Rep(G) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group G. For non-Abelian G, the symmetry is non-invertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain -- features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with non-trivial internal Hilbert spaces and fusion rules. Our work identifies properties of non-invertible symmetry breaking that existing quantum hardware can probe.
Physics Seminar: Elliott Gesteau
Time: 2:00 PM - 3:00 PM
Location: 313
Title: When can spacetime emerge? Â Â
Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a usual holographic correspondence. In this talk, I will explain how one can get to this conclusion by using either quantum information theory or properties of the large N limit of AdS/CFT, and propose a criterion for detecting failures of spacetime emergence. If time permits, I will also comment on the connection to recent proposals for taking into account the presence of an observer in quantum gravity.
Title: When can spacetime emerge? Â Â
Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a usual holographic correspondence. In this talk, I will explain how one can get to this conclusion by using either quantum information theory or properties of the large N limit of AdS/CFT, and propose a criterion for detecting failures of spacetime emergence. If time permits, I will also comment on the connection to recent proposals for taking into account the presence of an observer in quantum gravity.
Math Event: Algebraic Geometry Seminar: Dmitry Zakharov - Extending the Prym-Torelli map via the tropical trigonal construction
Time: 4:00 PM - 5:00 PM
Location:
Speaker: Dmitry Zakharov
Abstract: The Torelli map t_g:M_g->A_g associates to a smooth algebraic curve its Jacobian variety. Mumford and Namikawa proved that the Torelli map extends to a morphism from the Deligne-Mumford compactification of M_g to the second Voronoi compactification of A_g, and Alexeev showed that it also extends to the perfect cone compactification. The Prym-Torelli map p_g:R_g->A_{g-1} associates to an etale double cover of algebraic curves its Prym variety. Unlike the case of Jacobians, p_g does not extend to the natural compactification of R_g by the space of admissible double covers. The indeterminancy locus of p_g was completely characterized by Friedman and Smith, and a natural question is to determine the blowups that are needed to extend p_g to the various toroidal compactifications of A_{g-1}. I will explain an approach to this problem using the trigonal construction, which has algebraic and tropical versions. In particular, I will explain how to fully resolve the indeterminacy of the Prym-Torelli map to the second Voronoi compactification in the case g=4. As a companion result, I will explain how to compute the second moment of the tropical Prym variety in this case, a quantity which has arithmetic significance.
Speaker: Dmitry Zakharov
Abstract: The Torelli map t_g:M_g->A_g associates to a smooth algebraic curve its Jacobian variety. Mumford and Namikawa proved that the Torelli map extends to a morphism from the Deligne-Mumford compactification of M_g to the second Voronoi compactification of A_g, and Alexeev showed that it also extends to the perfect cone compactification. The Prym-Torelli map p_g:R_g->A_{g-1} associates to an etale double cover of algebraic curves its Prym variety. Unlike the case of Jacobians, p_g does not extend to the natural compactification of R_g by the space of admissible double covers. The indeterminancy locus of p_g was completely characterized by Friedman and Smith, and a natural question is to determine the blowups that are needed to extend p_g to the various toroidal compactifications of A_{g-1}. I will explain an approach to this problem using the trigonal construction, which has algebraic and tropical versions. In particular, I will explain how to fully resolve the indeterminacy of the Prym-Torelli map to the second Voronoi compactification in the case g=4. As a companion result, I will explain how to compute the second moment of the tropical Prym variety in this case, a quantity which has arithmetic significance.
Thursday, March 26th, 2026
Program Talks: Diego Liska
Time: 11:15 AM - 12:45 PM
Location: SCGP 313
Title: A universal sum over topologies in 3d gravity
Abstract: A careful analysis of the sum over topologies in 2d gravity led to an averaged form of the holographic correspondence: pure 2d gravity is dual to random matrix theory rather than to a single Hamiltonian. In this talk, I go one dimension higher and study the sum over topologies in 3d gravity and its relation to the statistical interpretation of the boundary theory. I formulate a statistical version of the conformal bootstrap that organizes universal properties of CFT data, namely typicality and crossing symmetry. I then identify a set of surgery moves on bulk manifolds that directly reflect these properties. These moves generate non-handlebodies, produce only hyperbolic manifolds, and do not generate all hyperbolic manifolds. This indicates a large range of possible choices for which manifolds may be included in the gravitational path integral, reflecting a broad class of ensembles consistent with crossing symmetry and typicality. Based on work with Alexandre Belin, Scott Collier, Lorenz Eberhardt and Boris Post (arXiv:2601.07906).
Title: A universal sum over topologies in 3d gravity
Abstract: A careful analysis of the sum over topologies in 2d gravity led to an averaged form of the holographic correspondence: pure 2d gravity is dual to random matrix theory rather than to a single Hamiltonian. In this talk, I go one dimension higher and study the sum over topologies in 3d gravity and its relation to the statistical interpretation of the boundary theory. I formulate a statistical version of the conformal bootstrap that organizes universal properties of CFT data, namely typicality and crossing symmetry. I then identify a set of surgery moves on bulk manifolds that directly reflect these properties. These moves generate non-handlebodies, produce only hyperbolic manifolds, and do not generate all hyperbolic manifolds. This indicates a large range of possible choices for which manifolds may be included in the gravitational path integral, reflecting a broad class of ensembles consistent with crossing symmetry and typicality. Based on work with Alexandre Belin, Scott Collier, Lorenz Eberhardt and Boris Post (arXiv:2601.07906).
Della Pietra Technical Talk by Persi Diaconis
Time: 2:00 PM - 3:00 PM
Location: 102
Abstract: pick a random graph on n points by flipping a fair coin for each possible edge. Now do it again, independently. What's the chance the two graphs you get are isomorphic? Small? How small? When n= 100, less than 10^(-1300). Now, let n = infinity. Pick two graphs at random. the chance that they are isomorphic is one (!). this is THE random graph. I will illustrate its strange properties by studying random walk. This is a typical problem of probability in the presence of a random geometry. I will introduce 'Hardy's inequalities' for trees to get where we need to go. This is joint work with Sourav Chatterjee and Laurent Miclo.
Abstract: pick a random graph on n points by flipping a fair coin for each possible edge. Now do it again, independently. What's the chance the two graphs you get are isomorphic? Small? How small? When n= 100, less than 10^(-1300). Now, let n = infinity. Pick two graphs at random. the chance that they are isomorphic is one (!). this is THE random graph. I will illustrate its strange properties by studying random walk. This is a typical problem of probability in the presence of a random geometry. I will introduce 'Hardy's inequalities' for trees to get where we need to go. This is joint work with Sourav Chatterjee and Laurent Miclo.
Friday, March 27th, 2026
Program Talks: Soumyadeep Chaudhuri
Time: 11:15 AM - 12:45 PM
Location: SCGP 313
Title: Semiclassical analysis of finite cut-off JT gravity on a disk
Abstract: In this talk I will present the computation of the partition function of finite cut-off JT gravity (with positive, zero or negative curvature) defined on a disk and coupled to conformal matter with central charge c. The analysis is done in a regime where c is a large negative number, while the magnitude of the cosmological constant scales linearly with |c| and the length of the boundary of the disk is kept finite. In this regime, the gravitational path integral is dominated by a smooth geometry corresponding to a saddle point of the action. By systematically taking into account the quantum fluctuations about this saddle point, one can obtain a perturbative expansion of the partition function in powers of 1/|c|. I will present the results for the leading and the first subleading terms in this expansion.
Title: Semiclassical analysis of finite cut-off JT gravity on a disk
Abstract: In this talk I will present the computation of the partition function of finite cut-off JT gravity (with positive, zero or negative curvature) defined on a disk and coupled to conformal matter with central charge c. The analysis is done in a regime where c is a large negative number, while the magnitude of the cosmological constant scales linearly with |c| and the length of the boundary of the disk is kept finite. In this regime, the gravitational path integral is dominated by a smooth geometry corresponding to a saddle point of the action. By systematically taking into account the quantum fluctuations about this saddle point, one can obtain a perturbative expansion of the partition function in powers of 1/|c|. I will present the results for the leading and the first subleading terms in this expansion.
Program Talks
Time: 2:00 PM - 3:30 PM
Location: SCGP 313
Title: A single geometry from an all-genus expansion in quantum gravity
Speaker: Wayne W. Weng
Abstract: In this talk, I will discuss an instance in quantum gravity where a topological expansion resums into an effective description on a single geometry. The original theory whose gravitational path integral we study is JT quantum gravity with one asymptotic boundary at nonperturbatively low temperatures. The effective theory we derive is a deformation of JT gravity by a highly quantum and nonlocal interaction for the dilaton, evaluated only on a disk topology. This emergent description addresses a strongly quantum gravitational regime where all genera contribute at the same order, successfully capturing the doubly nonperturbative physics of the original theory.
Title: A single geometry from an all-genus expansion in quantum gravity
Speaker: Wayne W. Weng
Abstract: In this talk, I will discuss an instance in quantum gravity where a topological expansion resums into an effective description on a single geometry. The original theory whose gravitational path integral we study is JT quantum gravity with one asymptotic boundary at nonperturbatively low temperatures. The effective theory we derive is a deformation of JT gravity by a highly quantum and nonlocal interaction for the dilaton, evaluated only on a disk topology. This emergent description addresses a strongly quantum gravitational regime where all genera contribute at the same order, successfully capturing the doubly nonperturbative physics of the original theory.