Calendar
- 28April 28, 2024No events
- 29April 29, 2024
Workshop on Global Categorical Symmetries
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)Participation in the workshop is by invitation.
CMSA Colloquium: The DNA of Particle Scattering
20 Garden Street, Cambridge, MA 02138At the Large Hadron Collider, the copious scattering of quarks and gluons in quantum chromodynamics (QCD) produces Higgs bosons and many backgrounds to searches for new physics. At short distances, scattering in QCD can be evaluated in perturbation theory and leads to highly intricate, multivariate mathematical functions such as generalized polylogarithms. To gain further insight, one can study a cousin of QCD called planar N=4 super-Yang-Mills theory. Some processes in this theory can be computed to eighth order in perturbation theory, versus second or third order in QCD. The computation and analysis of these results rely on a Hopf algebra coaction on polylogarithms. Its maximal iteration is called the `symbol’, which serves as a `genetic code’ for amplitudes. The symbol is a linear combination of words, sequences of letters analogous to sequences of DNA base pairs. Understanding the alphabet, and then reading the code, exposes the physics and mathematics of quantum scattering, including bizarre new symmetries. For example, the two scattering amplitudes that are known to the highest orders in perturbation theory (8 loops) are related to each other by an `antipodal duality’, which involves reading the code backwards as well as forwards. A third scattering amplitude, which contains the other two as limits, has an antipodal self-duality which `explains’ the other duality. However, we still don’t know `who ordered’ this property, or what it really means.
- 30April 30, 2024
Workshop on Global Categorical Symmetries
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)Participation in the workshop is by invitation.
Harvard-MIT Algebraic Geometry Seminar: Campana rational connectedness
The notion of Campana points were introduced by Campana and Abramovich, which interpolate between rational points and integral points. In this talk, we will focus on the geometric side and introduce Campana rational connectedness — a version of rational connectedness for varieties with simple normal crossings boundaries. We further prove that over function fields, weak approximations by Campana points at good places hold assuming Campana rational connectedness of fibers, generalizing a theorem of Hassett and Tschinkel. We further verify Campana rational connectedness for many basic examples. Our approach relies on the theory of stable log maps and their moduli. This is a joint work in progress with Brian Lehmann and Sho Tanimoto.
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For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
Introductory Math Seminar: Choosing Your First Math Class
Dr. Monique Harrison will be sharing her work with the Harvard Math Department, the conclusion of a survey and interview study in the Fall 2023 semester. Math courses at Harvard serve the majority of undergraduates who matriculate and often can have large impacts on subsequent student decision-making. She will discuss the findings of this study, which targeted first-year course selection and course experiences. Implications for department and university policies will be discussed.
- 01May 1, 2024
Workshop on Global Categorical Symmetries
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)Participation in the workshop is by invitation.
Number Theory Seminar: Modularity of special cycles in orthogonal and unitary Shimura varieties
1 Oxford Street, Cambridge, MA 02138 USASince the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms. In this talk, I will explain an extension of these results to toroidal compactifications where we prove that the generating series of divisors is a mixed mock modular form. This recovers and refines earlier results of Bruinier and Zemel. The results of this talk are joint work with Philip Engel and François Greer.
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For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html
Dynamics, Geometry and Moduli Spaces Seminar: Counting minimal surfaces in hyperbolic 3-manifolds
See webpage for more details: https://people.math.harvard.edu/~ctm/sem/
Richard P. Stanley Seminar in Combinatorics: Toric Matroid Bundles
Toric matroid bundles are combinatorial objects which serve as a tropical analogue to vector bundles over toric varieties. I’ll explain how to construct toric matroid bundles, how to check if a toric matroid bundle is globally generated or ample, and how to compute the characteristic classes of a toric matroid bundle in the T-equivariant chow cohomology of the base. Finally, I’ll show that each matroid determines a tautological toric matroid bundle over the permutahedral toric variety. I’ll discuss some properties of these bundles, and I’ll show that the characteristic classes of the tautological toric matroid bundle recover the tautological classes of matroids used by Berget, Eur, Spink, and Tseng to prove log-concavity properties of the Tutte polynomial.
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For more info, see https://math.mit.edu/combin/
- 02May 2, 2024
Workshop on Global Categorical Symmetries
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)Participation in the workshop is by invitation.
CMSA Active Matter Seminar: Control of parametric amplification in space-time modulated mechanical metamaterials
Active mechanical metamaterials harbor acoustic signal processing functionalities that are impossible to achieve in passive structures. Amplifying an elastic wave as it passes through the material is a prominent example, with potential applications in acoustic signal processing and loss mitigation. The fundamental mechanism for signal amplification of this kind is the parametric amplifier–an oscillator whose stiffness is periodically modulated in time, which can inject energy into mechanical oscillations. Typically, parametric amplification occurs at distinct modulation frequencies that are trivially related to the resonance modes of the unmodulated system, which restricts its utility for amplifying signals with complex spatial or spectral structure. In this talk, I’ll show how spatial variation of the modulation phase in parametric oscillator networks enables amplification phenomena that are far richer than those achievable by uncoupled and uncoordinated parametric amplifiers. Examples include turning off parametric resonances for particular vibrational modes in small assemblies [1], and achieving nonreciprocal broadband amplification in periodic arrays [2]. The existence of parametric resonances is tied to the internal symmetries inherent to mechanical systems as well as the symmetries obeyed by the parametric variation in space and time, through an exact theoretical framework that augments the standard Floquet analysis of space-time modulated systems.
[1] Melkani and Paulose, arXiv:2310.08734[2] Kruss and Paulose, PRApplied17, 024020 (2022)This seminar will be held in person and on Zoom.
https://harvard.zoom.us/j/96657833341
Password: cmsa
Symmetry Colloquia – Global Categorical Symmetries: Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry
20 Garden Street, Cambridge, MA 02138We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum.
https://cmsa.fas.harvard.edu/event/gcs24_cordova/
Symmetry Colloquia – Global Categorical Symmetries: Symmetries, Invertible Field Theories, and Gauge Theory Phases
20 Garden Street, Cambridge, MA 02138I will start with a brief overview of gauge theory phases in 3+1 dimensions through the lens of higher symmetries — in particular the realization of 1-form symmetries acting on loop order parameters. I will then review recent progress in refining this characterization using invertible field theories, or equivalently symmetry protected topological phases (SPTs). This refinement leads to new results in gauge theories with fundamental matter, such as quantum chromodynamics (QCD), which do not possess 1-form symmetries. I will explain why these theories must sometimes undergo a phase transition between their confining and Higgs regimes, despite the fact that classic results and standard lore say they should be continuously connected.
https://cmsa.fas.harvard.edu/event/gcs24_dumitrescu/
Symmetry Colloquia – Global Categorical Symmetries: The universal target category
20 Garden Street, Cambridge, MA 02138Hilbert’s Nullstellensatz says that the complex numbers C satisfy a universal property among all R-algebras: every not-too-large nonzero commutative R-algebra maps to C. Deligne proved a similar statement in categorical dimension 1: every not-too-large symmetric monoidal category over R maps to the category sVec of super vector spaces. In other words, sVec (and not Vec!) is “algebraically closed”. These statements help explain why quantum field theory requires imaginary numbers and fermions. I will describe the universal symmetric monoidal higher category that extends the sequence C, sVec, …. This is joint work in progress with David Reutter, and builds on closely-related work by GCS collaborators Freed, Scheimbauer, and Teleman and Schlank et al.
https://cmsa.fas.harvard.edu/event/gcs24_johnson-freyd/
- 03May 3, 2024
Workshop on Global Categorical Symmetries
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)Participation in the workshop is by invitation.
**CANCELED** Richard P. Stanley Seminar in Combinatorics: Polynomial Plank Problems
I will discuss the following result and its complex analog: For every nonzero polynomial P∈ R[x_1,…, x_n] of degree n, there is a point of the unit ball in R^d at distance at least 1/n from the zero set of the polynomial P. Joint work with Alexey Glazyrin and Roman Karasev.
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For more info, see https://math.mit.edu/combin/
- 04May 4, 2024No events