2026 Ding Shum Lecture: Sanjeev Arora, Princeton
2026-03-04 16:00 - 17:00 (America/New_York) | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
2026 Ding Shum Lecture
Date: March 4, 2026
Time: 4:00 pm
Location: Harvard Science Center Hall D & via Zoom Webinar
Speaker: Sanjeev Arora, Princeton
Title: How could a Superhuman AI mathematician come about?

Abstract: Can AI systems exceed the capabilities of the human experts who provided their training data? The talk will examine the hypothesis of AI self‑improvement, involving mechanisms such as synthetic data generation, reinforcement learning, and tool‑augmented reasoning with formal verification loops.
I will also present recent work at Princeton, including the Gödel Prover V2 for Lean‑based theorem proving and a new inference pipeline that achieved state‑of‑the‑art performance (at the time of evaluation) on IMO‑ProofBench (Advanced) at moderate inference costs ($20–$30 per problem). These will illustrate how AI systems are sometimes able to escape “cognitive wells”—local optima in a model’s reasoning capabilities. While providing evidence for the feasibility of self‑improvement, they also highlight important hurdles and open questions.

Sanjeev Arora is Charles C. Fitzmorris Professor of Computer Science and Director of Princeton Language and Intelligence, a unit devoted to research and applications of large AI models. He got his Phd from UC Berkeley in 1994 and has been a faculty member at Princeton since then. He has been awarded the ACM Prize in Computing (2011), Fulkerson Prize in Discrete Mathematics (2012), Packard Fellowship, Sloan Fellowship, and the ACM Doctoral Dissertation Prize. He was a plenary speaker at the International Congress of Mathematicians in 2018 and is a member of the National Academy of Science and American Academy of Arts and Sciences.

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

Fukaya categories and higher representation theory
2026-03-05 13:30 - 14:30 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Differential Geometry and Physics Seminar
Speaker: Vivek Shende (Syddansk Universitet & UC Berkeley)
Title: Fukaya categories and higher representation theory
Abstract: I will explain how Lagrangian Floer homology in certain monopole moduli spaces recovers the Khovanov homology and its relatives, by a description strikingly similar to the Oszvath-Szabo Heegard-Floer theory. I will also explain how the ‘sectorial descent’ of Fukaya categories can be used to construct Rouquier’s promised monoidal structure on the category of representations of the categorified “positive part” of the quantum group. This is joint work with Mina Aganagic, Elise LePage, and Peng Zhou.
Note: Location change to Harvard Science Center Room 300H

Freedman Seminar: Mattie Ji, Penn and Jeongwan Haah, Stanford
2026-03-06 15:00 - 17:15 | Hybrid
Freedman Seminar
Speakers: Mattie Ji (Penn) and Jeongwan Haah (Stanford)
Mattie Ji Title: Quantum Cellular Automata via Algebraic K-Theory
Abstract: Algebraic K-theory, on a very high level, is the study of how to break apart and assemble objects linearly, which makes the field amenable to classification questions. In this work, we apply this methodology to study the classification of quantum cellular automata (QCA). Over an arbitrary commutative ring R and a general class of metric spaces X, we construct a space of QCA that depends only on the large-scale (coarse) geometry of X. We explain how QCA classification groups (QCA modulo circuits) either arise naturally as or are refined by this space in most cases of interest.
Motivated by negative K-theory, we also show the classification of QCA on Euclidean lattices is given by an $Omega$-spectrum indexed by the dimension. As a corollary, we also obtain a non-connective delooping of the K-theory of Azumaya R-algebras, whose negative homotopy groups are the QCA classification groups. When R is the complex numbers, our method can be adapted to yield an $Omega$-spectrum for QCA of $C^*$-algebras with unitary circuits. This talk is based on joint work with Bowen Yang.

Jeongwan Haah Title: Fermionic QCA in 2d are trivial
Abstract: We consider bounded spread automorphisms of Z/2-graded algebra (fermionic QCA) on the two-dimensional lattice and prove that every fQCA is a unitary circuit followed by fermionic shifts when stabilized by Majorana modes. This is an analog of a theorem by Freedman and Hastings for the case of ungraded algebras. The overall argument follows a similar line in that we show invertible subalgebras in 1d is trivial, but the stabilization is used crucially. By an existing argument, this triviality of fQCA in 2d implies that the 3d (bosonic) QCA that disentangles the Walker-Wang model with three-fermion theory is nontrivial. The latter was known to be nontrivial against Clifford gates but remained conjectural against more general unitary gates. To my knowledge, this gives the only example ungraded QCA that is proved to be nontrivial against general unitary circuits and shifts, and the only example ungraded invertible subalgebra that is not isomorphic to any tensor product algebra. I will explain elements new to the fermionic setting and give an overview of the nontriviality argument. (Based on an upcoming work with Jeffrey Kwan and David Long)

The categorical 't Hooft expansion
2026-03-09 15:00 - 16:00 | Virtual
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Davide Gaiotto (Perimeter Institute)
Title: The categorical ‘t Hooft expansion
Abstract: The ‘t Hooft expansion is the key structure underlying dualities between gauge theories of large matrices and string theories. I will review categorical aspects of the ‘t Hooft expansion, matching the formal deformation space of certain “fundamental modifications” of the gauge theory to the formal deformation space of a category of boundary conditions (“D-branes”) for a 2d dg-TFT, to be identified with the world-volume theory for the string theory. I will illustrate this by reviewing the holographic description of matrix models.

CMSA/Tsinghua Math-Science Literature Lecture: Martin Bridson: Profinite rigidity: Chasing finite shadows of infinite groups
2026-03-10 08:45 - 10:15
CMSA/Tsinghua Math-Science Literature Lecture

Date: March 10, 2026
Time: 8:45 – 10:15 am ET
Location: Harvard Science Center Hall A, 1 Oxford Street, Cambridge MA & via Zoom Webinar
Speaker: Martin Bridson FRS is the Whitehead Professor of Pure Mathematics at Oxford and President of the Clay Mathematics Institute.
Title: Profinite rigidity: Chasing finite shadows of infinite groups
Abstract: There are many situations in geometry or elsewhere in mathematics where it is natural or convenient to explore infinite groups of symmetries via their actions on finite objects. But how hard is it to find these finite manifestations and to what extent does the collection of all such actions determine the infinite group?
In this talk, I will sketch some of the rich history of such problems and then describe some of the significant advances in recent years.
We’ll pay particular attention to groups that arise in 3-dimensional geometry and topology.

Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

TQFTs do not detect the Milnor sphere
2026-03-10 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Lorenzo Riva, Harvard CMSA
Title: TQFTs do not detect the Milnor sphere
Abstract: I will talk about the recent paper of Gripaios and Randall-Williams with that title, where they prove that a functorial TQFT (i.e. a symmetric monoidal functor from the n-dimensional bordism category into a suitably nice target category) assigns the same value to homotopy spheres that bound a parallelizable manifold, extending some no-go theorems of Reutter and Schommer-Pries.

Millennium Prize Problems Lecture - Javier Gómez-Serrano: Navier-Stokes Existence or Breakdown
2026-03-11 17:00 - 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Date: March 11, 2026
Time: 5:00–6:00 pm
Location: Harvard Science Center Hall C, 1 Oxford St., Cambridge MA & via Zoom Webinar
Speaker: Javier Gómez-Serrano, Brown University
Title: Navier-Stokes Existence or Breakdown
Abstract: The Navier-Stokes equations have been the cornerstone of fluid dynamics for over a century, accurately describing the motion of viscous fluids such as water and air. However, despite their fundamental importance to mathematics and physics, a profound question remains unanswered: do solutions to these equations always exist for all time, or can they break down and develop singularities (points where the equations lose their validity)? In this Millennium Prize Problems Lecture, I will explore the current mathematical landscape surrounding the Navier-Stokes and related equations. The talk will discuss the historical context, the ongoing search for global regularity versus finite-time blowup, and the latest analytical and computational breakthroughs pushing the boundaries of what we know about fluid behavior.
Read more about the Navier-Stokes Equation at the Clay Math website.

Organizers: Martin Bridson, Clay Mathematics Institute | Dan Freed, Harvard University and CMSA | Mike Hopkins, Harvard University

Millennium Prize Problems Lecture Series

Strongly adapted contact geometry of Anosov 3-flows
2026-03-12 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Surena Hozoori (Brandeis)
Title: Strongly adapted contact geometry of Anosov 3-flows
Abstract: We will discuss some recent developments in the contact geometric theory of Anosov 3-flows, whose roots go back to the works of Mitsumatsu and Eliashberg-Thurston in the mid 1990s. In particular, we provide a contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics, as well as investigate the basic properties of the resulting geometries. Time permitting, we will discuss how these results allow one to re-approach some classical questions in Anosov dynamics.

Finite N indices from branes and negative branes
2026-03-16 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Kasia Budzik (Harvard University)
Title: Finite N indices from branes and negative branes
Abstract: Finite-N effects in large-N gauge theories, such as trace relations, are expected to be holographically dual to non-perturbative phenomena in string theory, such as Giant Graviton branes. A convenient setting to study these effects are supersymmetric indices of U(N) gauge theories. The finite-N indices can be reproduced by a series of corrections to the infinite-N result, known as the Giant Graviton expansion.
In this talk I will present a generalization of the Molien-Weyl formula computing generating functions of invariants of supergroups U(N|M), which arise as gauge groups of brane/negative brane systems in string theory. The formula leads to a new expansion relating finite-N and infinite-N indices of U(N) gauge theories. I will comment on its relation to Murthy’s Giant Graviton expansion and suggest a physical interpretation in terms of branes and negative branes. This talk is based on arXiv:2509.20451 and work in progress with Davide Gaiotto.

Dynamic reasoning
2026-03-18 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Emmanuel Abbé, EPFL, Institute of Mathematics and School of Computer and Communication Sciences & Apple
Title: Dynamic reasoning
Abstract: In the current AI landscape, reasoning is frequently equated with the generation of intermediate “thinking traces”. However, these traces are merely a mechanism, not the ultimate objective.
Relying solely on the presence of a trace can be deceptive, as models often learn to mimic the format of reasoning while effectively overfitting to specific training distributions.
To build more robust and versatile reasoners, we shift our focus to more specific structural properties of the thinking process, in particular compositionality (inductive CoT, AdaBack) and abstraction (AbstRaL).

Moduli of subcanonical points
2026-03-19 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Dawei Chen, Boston College
Title: Moduli of subcanonical points
Abstract: Subcanonical points are special Weierstrass points on smooth algebraic curves whose semigroups are symmetric. In this talk, I will explain the rich geometry of the moduli space of subcanonical points, with a focus on its connected components, birational geometry, topology, and the deformation theory of related monomial singularities.

Line operators in holomorphic QFT
2026-03-24 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Keyou Zeng (CMSA)
Title: Line operators in holomorphic QFT
Abstract: We will discuss the recent work (arxiv:2508.11749), which defines the so called dg shifted Yangian. I will discuss their origin from the study of 3d holomorphic topological field theories, a variant of 3d TQFT. A dg shifted Yangian is supposed to control the fusion of line defect in the corresponding 3d HT theories. I will illustrate these discussions in examples.

Gauge theory on Hyperkähler manifolds
2026-03-26 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker. Emily Autumn Windes (New Uzbekistan University)
Title: Gauge theory on Hyperkähler manifolds
Abstract: In this talk, I describe various distinguished classes of connections on Hyperkähler manifolds and their dimensional reductions. Then, I describe a construction of new examples of Sp(2)-instantons, primitive HYM connections, and Spin(7)-instantons with symmetry on the manifold T*CP2. This talk is based on joint work with Jesse Madnick and Izar Alonso.

The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields
2026-03-26 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Matt Broe, Boston University
Title: The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields
Abstract: The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of L-functions. We prove the conjecture for certain classes of non-isotrivial varieties over Fq(t), including some cubic threefolds and fivefolds. We deduce the Birch and Swinnerton-Dyer conjecture for their intermediate Jacobians, and use it to establish new cases of the Tate conjecture over finite fields.

Exotic R^4's are unclassifiable
2026-03-27 15:00 - 17:15 | Virtual
Freedman Seminar
Speaker: Robert Gompf, UT Austin
Title: Exotic R^4’s are unclassifiable
Abstract: We will use descriptive set theory to show that there is a precise sense in which exotic R^4’s are unclassifiable. For other open manifolds, we can reach a much higher level of unclassifiability. This is work in progress with Aristotelis Panagiotopoulos.

K-theoretic stable envelopes, quantum loop groups and wall-crossings
2026-03-30 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Tianqin Zhu, Columbia University
Title: K-theoretic stable envelopes, quantum loop groups and wall-crossings
Abstract: The stable envelope is an important tool in both geometric representation theory and the enumerative geometry. One of the most important application is that it generates the geometric quantum loop group via the FRT formalism. In this talk, we will show that the geometric quantum loop group is isomorphic to the Drinfeld double given by the preprojective K-theoretic Hall algebra and the nilpotent K-theoretic Hall algebra. Moreover we will show a more refined result that the wall-crossing for the K-theoretic stable envelope is controlled by the universal R-matrix for the slope subalgebra of the Drinfeld double, which leads to the isomorphism between the wall subalgebra in geometric quantum loop groups and the slope subalgebras in the Drinfeld double. If time permits, I will talk about the recent progress of such isomorphism in the case of the critcial stable envelopes in both critical K-theory and critical cohomology. This is based on the work 2511.02161

1-shifted Yangians from 1-shifted Lie bialgebras
2026-03-31 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Vasily Krylov, Harvard
Title: 1-shifted Yangians from 1-shifted Lie bialgebras
Abstract: In the previous talk, Keyou explained that the fusion of line defects in 3d holomorphic–topological field theories is expected to be governed by so-called DG-shifted Yangians. Following arXiv:2503.08770, I will present examples of such DG-shifted Yangians arising from 1-shifted Lie bialgebras. We will discuss both the classical and DG-shifted settings from a purely mathematical perspective.

CMSA Q&A Seminar: Lauren Williams, Harvard
2026-04-01 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Lauren Williams, Harvard
Topic: The First Proof Project

Failures of Holographic Emergence
2026-04-03 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Elliott Gesteau, CMSA
Title: Failures of Holographic Emergence
Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a 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.

Twistorial constructions of higher genus integrability
2026-04-06 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Seraphim Jarov, Perimeter Institute
Title: Twistorial constructions of higher genus integrability
Abstract: I will present a new method to engineer integrable models in 4d with higher genus spectral parameters. The method has a twistorial origin – by working on a branched covering of twistor space, I show how one can derive deformations of holomorphic BF theory on twistor space which descend to elliptic and hyperelliptic models on R^4 via the Penrose transform. I show how one can bootstrap the Penrose transformed actions using symmetry and integrability to find deformations of self-dual Yang-Mills theory. I will also discuss some novel deformations of a BF type description of Hitchin’s equations. This is based on my paper: 2509.12486

Facets of link homology
2026-04-06 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Mikhail Khovanov, Johns Hopkins University
Title: Facets of link homology
Abstract: We will review some link homology theories of algebraic origin and their connections to representation theory and geometry.

A Mumford form on infinite Grassmannians
2026-04-07 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Oswaldo Vázquez (Harvard)
Title: A Mumford form on infinite Grassmannians
Abstract: The Polyakov measure in bosonic string theory can be expressed in terms of the Mumford form, which is a trivializing section of a product of determinant line bundles over the moduli space of genus g curves. We will discuss the work in https://arxiv.org/abs/2412.18570, which reviews how the moduli space can be embedded in an infinite dimensional Grassmannian as a Virasoro orbit and generalizes the Mumford form to other such orbits. In particular, this “universal Mumford form” can be described in terms of coordinates in the Grassmannian, which are amenable to computation and thus could have implications to the evaluation of amplitudes.

Multiplicities of graded families of ideals on Noetherian local rings
2026-04-09 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Dale Cutkosky, University of Missouri
Title: Multiplicities of graded families of ideals on Noetherian local rings
Abstract: Let $R$ be an arbitrary $d$-dimensional Noetherian local ring with maximal ideal $m_R$. In this talk, we give a generalization of the multiplicity $e(I)$ of an $m_R$-primary ideal $I$ of $R$ to a multiplicity $e(mathcal I)$ of a graded family of $m_R$-primary ideals $mathcal I$ in $R$. This multiplicity gives the classical multiplicity $e(I)$ if $mathcal I={I^n}$ is the $I$-adic filtration, and agrees with the volume, $lim_{nrightarrow infty}d!frac{ell(R/I_n) }{n^d}$ for $R$ such that $dim N(hat R)>d$, the required condition for the volume of graded families of $m_R$-primary ideals to exist as a limit. We will show that many of the classical theorems for the multiplicity of an ideal generalize to this multiplicity, including mixed multiplicities, the Rees theorem and the Minkowski inequality and equality. We give proofs which are independent of the theory of volumes and Okounkov bodies for all of our results, with the one exception being the proof of the Minkowski equality. We do this by interpreting the multiplicity of graded families of $m_R$-primary ideals as an intersection product on the family of $R$-schemes which are obtained by blowing up $m_R$-primary ideals in $R$.

Quantum topology from dynamics
2026-04-10 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Sunghyuk Park, CMSA
Title: Quantum topology from dynamics
Abstract: Dynamics studies the long-term behavior of systems that evolve over time, such as the famous Lorenz system.
Quantum topology, by contrast, studies knots and low-dimensional manifolds through invariants that are usually constructed using representation-theoretic tools. In this talk, I will explain how quantum invariants of knots and 3-manifolds can be recovered from the dynamics of certain three-dimensional flows. Time permitting, I will also explain how this new bridge arises from ideas in topological string theory.

Abelian gauge fields and duality
2026-04-14 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard Math & CMSA
Title: Abelian gauge fields and duality
Abstract: Motivated by the new paper arXiv:2603.19161, I will give a general talk about abelian gauge fields, including duality. I will start with classical Maxwell theory, then discuss various “finite” examples, the typical p-form abelian gauge field, and some exotic examples such as Ramond–Ramond fields and the B-field in superstring theory. I will then get to the new paper and, time permitting, will suggest a very general framework that covers all examples.

Swampland and our Universe
2026-04-15 08:00 - 2026-04-16 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Swampland and our Universe
Dates: April 15–16, 2026
Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA
The swampland program has inspired a range of new ideas in both cosmology and neutrino physics. This workshop brings together experts in neutrino physics, dark energy, dark matter, early-universe cosmology, and string theory to share insights on these developments and to discuss current and future experimental tests.
Speakers

Ignatios Antoniadis, IAS, Princeton
Alek Bedroya, Princeton
Mike Boylan-Kolchin, UT Austin
M.C. Gonzalez-Garcia, YITP Stony Brook & ICREA U. Barcelona
Mustapha Ishak-Boushaki, UT Dallas
Marc Kamionkowski, Johns Hopkins
Miguel Montero, Institute of Theoretical Physics, Madrid
Georges Obied, U Chicago
Matt Reece, Harvard
Tracy Slatyer, MIT

Organizers: Luis Anchordoqui (CUNY Lehman College), Sonia Paban (Harvard Physics), and Cumrun Vafa (Harvard Physics)

Videos are available on the CMSA Youtube Swampland Playlist
Schedule
(download pdf)
Wednesday, Apr. 15, 2026
8:00–9:00 am
Breakfast
9:00–10:00 am
Marc Kamionkowski, Johns Hopkins: Dark-matter dynamics and new physics
Abstract: Galactic halos that are spherical, stationary, and composed of collisionless dark matter are easy to describe mathematically. If dark matter decays or interacts or there is some departure from equilibrium or time evolution of the system, all bets are off. In this case costly N-body simulations are required. If, however, one retains the assumption of spherical symmetry, these systems can be evolved numerically with a far simpler algorithm that is easily coded run in a matter of minutes on a laptop, rather than a day on a supercomputer. I will describe this approach and illustrate with simulations of self-interacting dark matter, decaying dark matter (with and without anisotropic velocity distributions, supermassive-black-hole growth, tidal stripping, mixed SIDM/CDM models. Come prepared with your own non-standard dark-matter model; we’ll see if we can simulate it during the talk!
10:00–10:30 am
Coffee Break
10:30–11:30 am
Tracy Slatyer, MIT: What (more) the CMB can teach us about dark matter
Abstract: Observations of the cosmic microwave background have already provided critical evidence for dark matter, but can also stringently constrain a range of dark matter properties. I will outline CMB constraints on dark matter properties based on purely gravitational effects, and then discuss in more detail how both CMB anisotropies and the blackbody spectrum can be used to test dark matter interactions with the Standard Model.
11:30 am–1:00 pm
Lunch Break (catered)
1:00–2:00 pm
Alek Bedroya, Princeton: How Quantum Gravity Constrains Physics on the Largest Length Scales
Abstract: I will review the hierarchy of energy scales in quantum gravity, from the Hubble scale in the IR to the quantum-gravity cutoff and the Planck scale in the UV, and emphasize the nontrivial UV/IR relations that connect them. I will discuss conjectures constraining scalar potentials and explain how they are related to the behavior of the other energy scales, together with bottom-up arguments based on general principles of quantum gravity such as holography. In particular, I will explain how well-motivated holographic assumptions lead to strong restrictions on scalar potentials, ruling out parametrically prolonged accelerated expansion for positive potentials and obstructing parametric scale separation for negative potentials associated with AdS vacua. Title: How Quantum Gravity Constrains Physics on the Largest Length Scales
Abstract: I will review the hierarchy of energy scales in quantum gravity, from the Hubble scale in the IR to the quantum-gravity cutoff and the Planck scale in the UV, and emphasize the nontrivial UV/IR relations that connect them. I will discuss conjectures constraining scalar potentials and explain how they are related to the behavior of the other energy scales, together with bottom-up arguments based on general principles of quantum gravity such as holography. In particular, I will explain how well-motivated holographic assumptions lead to strong restrictions on scalar potentials, ruling out parametrically prolonged accelerated expansion for positive potentials and obstructing parametric scale separation for negative potentials associated with AdS vacua.
2:00–2:30 pm
Coffee Break
2:30–3:30 pm
Mustapha Ishak-Boushaki, UT Dallas: Persistent and serious challenge to the ΛCDM throne: Evidence for dynamical dark energy rising from combinations of different types of datasets
Abstract: We derive multiple constraints on dark energy and compare dynamical dark energy models with a time-varying equation of state (w0waCDM) versus a cosmological constant model (LCDM). We use Baryon Acoustic Oscillation (BAO) from DESI and DES, Cosmic Microwave Background from Planck with and without lensing from Planck and ACT (noted CMBL and CMB, respectively), supernovae(SN), and cross-correlations between galaxy positions and galaxy lensing from DES. We use pairs or triplets of datasets where we exclude one type of dataset each time and categorize them as “NO SN”, “NO CMB” and “NO BAO” combinations. In all cases, we find that the combinations favor the w0waCDM model over LCDM, with significance ranging from 2.0 to 3.0-sigma. The persistence of this pattern across various dataset combinations even when any of the datasets is excluded supports an overall validation of this trending result regardless of any specific dataset. Next, we use larger combinations of these datasets after verifying their mutual consistency within the w0waCDM model. We find combinations that give robust significance levels, with DESI+DESY6BAO+CMBL+SN giving 3.4-sigma. In sum, while we need to remain cautious, the trend and pattern of these results beyond any single type of dataset and their associated systematics presents a compelling overall portrait not in favor of the LCDM and constitutes a serious challenge to the model’s reign. A few other cosmological results will be provided.
3:30–4:00 pm
Coffee Break
4:00–5:00 pm
Georges Obied, U Chicago: The Dark Dimension and its interplay with DESI data
Abstract: In this talk, I will discuss the motivation for considering an extra mesoscopic Dark Dimension of length l ~ 1 – 10 microns, taking into account theoretical and observational arguments. I will then talk about cosmological aspects of the Dark Dimension. In particular this scenario leads, by the universal coupling of the Standard Model sector to bulk gravitons, to massive spin 2 KK excitations of the graviton in the Dark Dimension (the “dark gravitons”) as an unavoidable dark matter candidate. Observations allow such an extra dimension of size in the micron range. Finally, I will discuss how this scenario can naturally accommodate features recently observed by the DESI survey such as an effective dark energy equation of state that is smaller than -1.

Thursday, Apr. 16, 2026
8:00–8:30 am
Breakfast
8:30–9:30 am
MC Gonzalez-Garcia, YITP Stony Brook & ICREA U. Barcelona: Massive Neutrinos in 2026: What we know, what we do not know (yet?), and what we do not understand
Abstract: In this talk I will present an update of the current understanding (and some not understanding) of the neutrino masses and the lepton mixing and some other minimal SM extensions as derived from direct scrutiny of the results of neutrino flavour oscillation experiments, some other laboratory probes, and the cosmos.
9:30–10:00 am
Coffee Break
10:00–11:00 am
Miguel Montero, IFT, Madrid: Neutrinos and B-L symmetry in the Dark Dimension scenario
Abstract: The Dark Dimension proposes the existe of a micrometer-sized large extra dimension, whose size is tied to the observed small vacuum energy. I will review the scenario, and then discuss how to embed the B-L global symmetry of the SM, focusing on one possibility which leads to an explanation of the observed coincidence between neutrino mass scale and the vacuum energy scale, while leading to 3 light species of right-handed neutrinos. I will also briefly discuss potential opportunities for detection of the resulting neutrino oscillations.
11:00–11:30 am
Coffee Break
11:30 am–12:30 pm
Ignatios Antoniadis, IAS, Princeton: Searching for the dark dimension in neutrino experiments
Abstract: Micron size extra dimensions offer a possibility to explain the smallness of neutrino masses if the right-handed neutrino propagates in the higher dimensional bulk. I will discuss the theoretical framework and the experimental signatures of this proposal in present and future experiments of KATRIN prototype, aiming to measure the magnitude of neutrino masses and to search for extra sterile-type species.
12:30–1:30 pm
Lunch Break (catered)
1:30–2:30 pm
Mike Boylan-Kolchin, UT Austin: Galaxies as Tracers of the Matter Density Field
Abstract: Galaxy formation is often (rightly) thought of as involving a complex interplay of messy astrophysical processes, but it also traces the nonlinear evolution of the matter density in the Universe. Remarkably, it appears that properties of this nonlinear field are intimately connected to properties of the initial linear fluctuations and some basic physics of dark matter interactions. I will explore some of these connections, with applications that include the surprisingly fast evolution of early galaxy formation as revealed by JWST and properties of the lowest-mass dark matter clumps capable of hosting galaxies in the local Universe.
2:30–3:00 pm
Coffee Break
3:00–4:00 pm
Matt Reece, Harvard: Axions from String Theory, and String Theory from Axions
Abstract: String theory compactifications contain the right ingredients to produce axion fields that might solve the Strong CP problem or contribute to dark matter or dynamical dark energy in our universe. After briefly reviewing some of these ingredients, I will frame the inverse question: suppose that an axion is discovered, and its decay constant is measured in an experiment. Could this help us to locate ourselves in the string landscape? In particular, I will discuss how an axion could give us clues about the fundamental string scale and the scale of supersymmetry breaking.

Millennium Prize Problems Lecture - Peter Sarnak: Riemann Hypothesis
2026-04-15 17:00 - 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Date: April 15, 2026
Time: 5:00–6:00 pm
Location: Harvard Science Center Hall C, 1 Oxford St., Cambridge MA
Speaker: Peter Sarnak, Institute for Advanced Study
Title: The Riemann Hypothesis
Abstract: After reviewing the hypothesis as put forth by Riemann we discuss its generalizations and analogues. We highlight a few of their implications and workarounds, and probing their truths.
Read more about the Riemann Hypothesis at the Clay Math website.
Organizers: Martin Bridson, Clay Mathematics Institute | Dan Freed, Harvard University and CMSA | Mike Hopkins, Harvard University

Millennium Prize Problems Lecture Series

Interpolation for points in $mathbb{P}^N, Ngeq 2$
2026-04-16 16:00 - 17:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Algebra Seminar
Speaker: Dipendranath Mahato, Tulane University
Title: Interpolation for points in $mathbb{P}^N, Ngeq 2$
Abstract: Interpolation problems study hypersurfaces in projective space passing through prescribed sets of points. Classically, one asks how many independent conditions a collection of points imposes on hypersurfaces of a fixed degree, a question that can be studied algebraically via homogeneous ideals and their Hilbert functions. In this talk, I will begin with the classical interpolation problem for reduced points and introduce the algebraic framework used to study it. I will then move to fat point schemes, where points are assigned multiplicities and hypersurfaces are required to vanish to higher order. In this setting, interpolation problems naturally lead to symbolic powers of ideals and containment relations between symbolic and ordinary powers. I will conclude by discussing open questions, including potential connections between interpolation problems and combinatorial structures such as matroids.

Higgs and Coulomb branches: Geometry and Representation Theory
2026-04-17 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Vasily Krylov
Title: Higgs and Coulomb branches: Geometry and Representation Theory
Abstract: Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. Quantized Coulomb branches are associative algebras deforming the algebras of functions on Coulomb branches. They are closely related to many important representation-theoretic structures, such as Yangians, quantum groups, and Hecke algebras. In this talk, I will discuss how 3D mirror symmetry, together with other insights motivated by physics, yields very explicit answers to purely representation-theoretic questions about representations of some of these quantum groups. Talk is based on joint works with Dinkins, Karpov, Klyuev, and Lance.

Zigzags, adjoints, and bordisms
2026-04-20 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Lorenzo Riva (Harvard CMSA)
Title: Zigzags, adjoints, and bordisms
Abstract: We will learn how to freely add adjoints to a category using a combinatorial procedure which involves drawing zigzags of squares. Peculiarly, we can use these to draw some bordisms. This is joint work with Martina Rovelli.
