CMSA

CMSA/MATH Welcome Back Gathering
2025-01-30 16:00 - 17:30 (America/New_York) | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Thursday, Jan. 30, 2025
4:00 pm
All CMSA and Math affiliates are invited.

Smooth projective fibrations over the projective line and their sections
2025-01-31 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Iacopo Brivio
Title: Smooth projective fibrations over the projective line and their sections
Abstract: Suppose $fcolon Xto mathbf{CP}^1$ is a smooth projective fibration, is it then true that $f$ has a section? This deceptively simple result was established by Seidel and McDuff using deep methods of symplectic geometry. Alex Pieloch recently generalized this to morphisms with at most one singular fibers and furthermore showed that $X$ uniruled, that is covered by images of $mathbf{P}^1$. In my talk I will explain how to recover Pieloch’s result from the Good Minimal Model Conjecture.

Topological to Gravitational Leptogenesis, via Ultra Unification
2025-02-03 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Juven Wang (LIMS, Royal Institution)
Title: Topological to Gravitational Leptogenesis, via Ultra Unification
Abstract: We propose a new mechanism for leptogenesis, named Topological Leptogenesis, in which dark matter consists of topological order, so gapped anyon excitations decay to generate the Standard Model lepton asymmetry. Topological Leptogenesis is in contrast with the Majorana Leptogenesis and Gravitational Leptogenesis. In the standard Majorana Leptogenesis, the baryon asymmetry of the present universe is attributed to the leptogenesis from the sterile right-handed neutrino with heavy Majorana fermion mass decaying into the Standard Model leptons in the very early universe, while the electroweak sphaleron causes baryogenesis at a later time. Gravitational leptogenesis can be regarded as an intermediate step between Majorana particle leptogenesis and topological non-particle leptogenesis. Topological Leptogenesis is derived out of Ultra Unification constructed from a mod 16 nonperturbative global anomaly cancellation that adds a symmetry-extended anomalous gapped topological quantum field theory (TQFT) to the Standard Model. Thus (1) the Beyond-the-Standard-Model (BSM) Dark Matter partly consists of Topological Order with low energy TQFT, while there are anyon string excitations above the energy gap. (2) The 5th force is a Topological Discrete Gauge Force of (B-L) that mediates between the Standard Model particles, the BSM Topological Order, and gapped anyon string non-particle excitations.
Based on https://arxiv.org/abs/2501.00607, https://arxiv.org/abs/2012.15860, https://arxiv.org/abs/2302.14862 and https://arxiv.org/abs/2411.05786.

Rational approximation and the AAA algorithm
2025-02-03 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Nick Trefethen, Harvard University
Title: Rational approximation and the AAA algorithm
Approximation by rational functions used to be mainly a theoretical subject, but with the introduction of the AAA algorithm in 2018, it became computationally practical and indeed easy. The implications for what we can do numerically are enormous. This talk will outline the algorithm and demonstrate its application to a collection of problems. We can also use it to demonstrate the potential theory that underlies the theory of rational approximation, a topic that goes back to Joseph Walsh here at Harvard a century ago.

The mass angular momentum inequality
2025-02-04 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Gilbert Weinstein, Ariel University
Title: The mass angular momentum inequality
Abstract: We show that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’, or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.

Blob homology
2025-02-04 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Sunghyuk Park, Harvard CMSA
Title: Blob homology

CMSA Q&A Seminar: Subir Sachdev
2025-02-05 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar

Speaker: Subir Sachdev, Harvard University
Topic: What is a quantum critical region?

Quantum algebras and R-matrices from the equivariant affine Grassmannians
2025-02-06 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Wenjun Niu, Perimeter Institute
Title: Quantum algebras and R-matrices from the equivariant affine Grassmannians
Abstract: 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.

Is every knot isotopic to the unknot?
2025-02-07 14:00 - 15:45 | Virtual
Freedman CMSA Seminar
*via Zoom*
Speaker: Sergey Melikhov, Steklov Math Institute
Title: Is every knot isotopic to the unknot?
Abstract: The following problem was stated by D. Rolfsen in his 1974 paper; according to R. Daverman it was being discussed since the mid-60s. Is every knot in $S^3$ isotopic (=homotopic through embeddings) to a PL knot — or, equivalently, to the unknot? In particular, is the Bing sling isotopic to a PL knot? We show that the Bing sling $B$ is not isotopic to any PL knot by an isotopy which extends to an isotopy of any 2-component link obtained from $B$ by adding a disjoint component $Q$ such that $lk(B,Q)=1$. Moreover, the assertion remains true if the additional component is allowed to self-intersect, and even to get replaced by a new one at any time instant $t$, as long as it remains disjoint from the original component $K_t$ and represents the same conjugacy class as the old one in $G/[G’,G”]$, where $G=pi_1(S^3setminus K_t)$. The are examples showing that the latter result cannot be improved in certain ways. I plan to present a sketch of the proof, modulo some ingredients. The details can be found in arXiv:2406.09365 and the main ingredients in arXiv:2406.09331 and arXiv:math/0312007v3.

Joint BHI/CMSA Foundation Seminar: Quantum Effects Inside Black Holes
2025-02-10 09:30 - 10:30 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint BHI/CMSA Foundation Seminar
Location: BHI seminar room
Speaker: Noa Zilberman (Princeton University)
Title: Quantum Effects Inside Black Holes
Abstract: Astrophysical black holes are known to be rotating. Within classical General Relativity, the simplest spacetime solution (the Kerr solution) describing a rotating black hole reveals a traversable passage through an inner horizon – which in turn may lead to another external universe. But does this remain the case when taking quantum effects into account?
Answering this question, along others, requires one to understand the manner in which quantum energy fluxes affect the internal geometry of a black hole. It has been widely anticipated, yet inconclusive (till this work), that such effects would diverge at the inner horizon of a spinning black hole. This divergence, if indeed takes place, may drastically affect the internal black hole geometry, potentially preventing the inner horizon traversability. Clarifying this issue requires the computation of the quantum energy fluxes in black hole interiors. However, this has been a serious challenge for decades.
Using a combination of old and new methods, we have managed to compute the quantum energy fluxes at the inner horizon of a spinning black hole, in a vacuum state corresponding to an evaporating black hole. We found that these fluxes are either positive or negative, depending on the black hole spin (and polar angle). The sign of these fluxes may be crucial to the nature of their backreaction on the geometry (as should be dictated by the semiclassical Einstein equation).
In this seminar, we shall briefly describe the basic framework of semiclassical general relativity and the renormalization procedure, and then present our novel results for the quantum fluxes at the inner horizon of a rotating black hole, briefly mentioning possible implications for the inner horizon traversability.

On 5d conformal matter
2025-02-10 11:00 - 12:00 | Virtual
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Mario De Marco (UL Brussels)
Title: On 5d conformal matter
Abstract: SCFTs with 8 supercharges lie at the sweet spot of the classification program of susy scale-invariant theories: with this amount of susy, the classification is in principle achievable, despite being non-trivial. In this talk, I will present the geometric approach to the classification of 5d SCFTs, based on geometric engineering on non-compact Calabi-Yau manifolds. The strategy is to imagine a 5d SCFT as a non-Lagrangian generalization of a quiver, and to build this generalised quiver by gauging together indecomposable blocks, called “5d conformal matter theories”. In this talk, I will start with a recap of the geometric construction of [2311.04984]. I will then present some forthcoming results, concerning the (p,q) web realization of 5d conformal matter theories, their reduction to 4d, their magnetic quiver, and the discovery of exotic “trifundamental” and “quadrifundamental” 5d indecomposable blocks (with flavor group at least SO(4k+2)^3 or SO(4k)^4).
In collaboration with M. Del Zotto, M. Graffeo, J. Grimminger, and A. Sangiovanni.

AI in math and theoretical physics: Status and prospects
2025-02-10 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Michael Douglas, Harvard CMSA
Title: AI in math and theoretical physics: status and prospects
Abstract: AI is making great progress and has the potential to change how we work in unprecedented ways. In this talk I will survey a few recent works which illustrate the state of the art, some from my own research, some developed at the CMSA’s recent program on Mathematics and Machine Learning. I will then report on current developments in AI and speculate on how they will affect our work in the next few years.

On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system
2025-02-11 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Liam Urban (University of Vienna)

Title: On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system
Abstract: In recent years, the formation of Big Bang singularities has been increasingly well understood in presence of scalar-field matter, which suppresses the geometric oscillations that one generically expects otherwise. From a cosmological perspective, however, one would like to understand whether this feature persists when coupled to further models that more closely resemble the matter content in our universe.
In this talk, I will discuss the past nonlinear stability of FLRW solutions to the Einstein scalar-field Vlasov system in three and four spacetime dimensions without symmetry assumptions. The latter is based on joint work with David Fajman. In both works, near-FLRW solutions are
shown to be asymptotically velocity term dominated toward the past, resulting in a quiescent Big Bang singularity with stable Kretschmann scalar blow-up. The Vlasov distribution, however, becomes highly anisotropic towards the Big Bang singularity, concentrating in preferred momentum directions associated with eigendirections of the shear. To ensure that the scalar field sufficiently mitigates this behaviour, one crucially exploits a scaling hierarchy between horizontal and vertical derivatives in the expansion normalized Vlasov equation. In four
spacetime dimensions, this analysis is paired with a Bel-Robinson energy formalism to control the spacetime and scalar field evolution, while one finds a significantly more direct proof in three dimensions since the spatial Riemann curvature is pure trace.
As a corollary, one also obtains that the Strong Cosmic Censorship conjecture holds for four-dimensional polarized $U(1)$-symmetric solutions to the Einstein vacuum equations with spatial topology $MtimesS^1$ and isotropic quotient.

Discussion of Integrating quantum groups over surfaces
2025-02-11 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Ben Gammage, Harvard University
Title: Discussion of Integrating quantum groups over surfaces
https://arxiv.org/abs/1501.04652

CMSA Q&A Seminar: Javier Gomez-Serrano
2025-02-12 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Javier Gomez-Serrano, Brown University
Topic: Please tell us about the Millennium prize problem for Navier-Stokes and segue from that into ML?

Discovering Data Structures: Nearest Neighbor Search and Beyond
2025-02-12 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Omar Salemohamed, Mila
Title: Discovering Data Structures: Nearest Neighbor Search and Beyond
Abstract: As neural networks learn increasingly sophisticated tasks—from image recognition to mastering the game of Go—we ask: can deep learning discover data structures entirely from scratch? We introduce a general framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. For nearest neighbor (NN) search, our model (re)discovers classic algorithms like binary search in one dimension and learns structures reminiscent of k-d trees and locality-sensitive hashing in higher dimensions. Additionally, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.

The Structure of the Flux Landscape
2025-02-13 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Damian Van de Heisteeg, Harvard CMSA
Title: The Structure of the Flux Landscape
Abstract: 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.

2025 Ding Shum Lecture: Irit Dinur, IAS: Expanders from local to global
2025-02-13 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On February 13, 2025 the CMSA hosted the sixth annual Ding Shum Lecture, given by Irit Dinur, Institute for Advanced Study.
Location: Harvard Science Center Hall A & via Zoom Webinar
Speaker: Irit Dinur, Institute for Advanced Study

Title: Expanders from local to global
Abstract: Imagine a network—like a social network, a transportation system, or even a biological system—where every part of the network is robustly connected to the rest. Expander graphs are the mathematical idealization of such networks. They are structures where any small group of points (nodes) has many connections to the rest of the graph, ensuring that no part is isolated and information (or influence) spreads efficiently throughout.
We will begin by surveying expander graphs, their discovery and construction, and some fascinating applications such as error-correcting codes, pseudorandomness, and probabilistically checkable proofs (PCPs), highlighting their role as a foundation for many breakthroughs in theoretical computer science. Then, we will shift focus to an exciting new kind of expanders called high dimensional expanders (HDXs). While expanders are well-understood and widely applied, HDXs remain enigmatic, with potential that we are only starting to uncover. We will talk about a fascinating local to global feature that HDXs have, and some applications.

This event is made possible by the generous funding of Ding Lei and Harry Shum.

Jack polynomials and enumeration of non-orientable maps
2025-02-14 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Houcine Ben Dali, Harvard CMSA
Title: Jack polynomials and enumeration of non-orientable maps
Abstract: A map is a graph embedded on a surface, which may be orientable or not. The representation theory of the symmetric group can be used to write the generating series of maps on orientable surfaces using Schur symmetric functions.
Several conjectures suggest that Jack polynomials—a one-parameter deformation of Schur functions—are related to the enumeration of non-orientable maps counted with a “non-orientability” weight. In this talk, I will discuss some of these conjectures and present recent progress in this direction.

General Relativity Seminar
2025-02-18 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Maximilian Ofner, University of Vienna
Title: Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes
Abstract: Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However, for FLRW models with a fast expansion rate, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results, complemented by numerical analysis.

Algebras of "symmetries" in QFT and applications to solitons (1)
2025-02-18 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard CMSA and Math
Title: Algebras of “symmetries” in QFT and applications to solitons (1)
https://arxiv.org/abs/2403.08883

CMSA Q&A Seminar: Phillip Matchett Wood
2025-02-19 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Phillip Matchett Wood, Harvard University
Topic: Info session on the CMSA/Mathematics Summer REU Program (Research Experience for Undergraduates)

The geometry of pure spinor superfield formalism
2025-02-20 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Simone Noja (Heidelberg University)
Title: The geometry of pure spinor superfield formalism
Abstract: 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.

Toward constructing a large-scale quantum computer based on TQFT
2025-02-24 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Liyuan Chen ( Harvard)
Title: Toward constructing a large-scale quantum computer based on TQFT
Abstract: Topological quantum computation, motivated by topological quantum field theory (TQFT), offers a promising path toward fault-tolerant universal quantum computation. However, the practical realization of such a system remains challenging due to the difficulty of finding suitable topological materials. In this work, we provide a comprehensive blueprint for constructing a fault-tolerant universal quantum computer based on the quantum double model $mathcal{D}(S_3)$, a specific non-Abelian topological order. We implement logical computations using quantum circuits on qubits and qutrits, including a single non-Clifford gate, compatible with near-term quantum devices. This work bridges the gap between abstract mathematical frameworks and noise-resilient quantum computation on near-term devices. Our proposal offers a promising path to realize a non-Abelian anyon-based large scale quantum computer.

BKL bounces outside homogeneity
2025-02-25 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Warren Li ( Princeton University)
Title: BKL bounces outside homogeneity
Abstract: In work spanning the late 20th century, physicists Belinski, Khalatnikov and Lifshitz (BKL) proposed a general ansatz for solutions to the Einstein (vacuum) equations near singularities. They suggest that the spacetime dynamics at different spatial points on the singularity decouple and are well-approximated by a system of autonomous nonlinear ODEs, whose orbits are governed by a chaotic cascade of “BKL bounces”. In this talk, we present recent work verifying BKL’s heuristics in a large class of symmetric, but spatially inhomogeneous, spacetimes. In particular, we prove decoupling even in the presence of (up to one) BKL bounce. The proof uses nonlinear ODE analysis coupled to hyperbolic energy estimates, and one hopes our methods may be applied more generally.

Algebras of "symmetries" in QFT and applications to solitons (2)
2025-02-25 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard CMSA and Math
Title: Algebras of “symmetries” in QFT and applications to solitons (2)
https://arxiv.org/abs/2403.08883

Datasets for Math: From AIMO Competitions to Math Copilots for Research
2025-02-26 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Simon Frieder, Oxford
Title: Datasets for Math: From AIMO Competitions to Math Copilots for Research
Abstract: This talk begins with a brief exposition of the AI Mathematical Olympiad (AIMO) on Kaggle, now in its second iteration, outlining datasets and models available to contestants. Taking a broader perspective, I then examine 1) the overarching issues the current datasets suffer from—such as binary evaluation or constrained sets of use cases— and 2) the trajectory they set for competition-style mathematical problem-solving, which is different from mathematical research practice. I argue for a fundamental shift in dataset structure and composition, both for training and evaluation, and introduce the idea of mapping mathematical workflows to data, a key example underscoring the need for this shift. I touch upon new thinking LLMs and their role in redefining LLM math evaluation, highlighting their implications for dataset design. Finally, I propose general improvements to the current state of mathematical datasets, including mathematical adaptations of dataset documentation (e.g., datasheets).

2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
2025-02-27 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Wei Bu (Harvard University)
Title: 2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
Abstract: In this talk, I will present a simple chiral 2d Lagrangian living on a 2d celestial sphere on the null boundary of 4d Minkowski space and briefly mention its first principal derivation using twistor theory. This 2d theory gives the asymptotic/edge dynamics of 4d (self-dual) Einstein gravity in asymptotically flat spacetimes. For example, using simple 2d CFT computations, one could recover generators of asymptomatic symmetries. If time permits, I’ll further discuss the potential of using this theory to produce a QFT computation of the entropy of a certain asymptotically flat black hole.

The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
2025-02-28 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Matteo Parisi
Title: The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
Abstract: The amplituhedron is the image of the positive Grassmannian—the region of the Grassmannian where all Plücker coordinates are nonnegative—under a totally positive linear map. It is a far-reaching generalization of cyclic polytopes and hyperplane arrangements, and the positive Grassmannian itself. The “volume” of the amplituhedron encodes probabilities of particle interactions in the quantum field theory N=4 super Yang-Mills, and calculating this volume involves decomposing (or tiling) the amplituhedron into smaller pieces (or tiles) and summing their volumes. This talk will delve into the rich combinatorics of these tiles and tilings, presenting recent results on some of the central conjectures in this area, including the magic number, BCFW tiling, and cluster adjacency conjectures.

Quantum Field Theory and Physical Mathematics
2025-03-03 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Kai Xu, Harvard
Title: Finite Landscape of 6d N=(1,0) Supergravity
Abstract: We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by T≤193, and the rank of the gauge group is restricted to r(V)≤480. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: h1,1(CY3)≤491, h1,1(Base)≤194 which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle.
