April | April | April | 1 - CMSA EVENT: Workshop on Global Categorical Symmetries
9:00 AM-5:00 PM May 1, 2024-May 3, 2024 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: Number Theory Seminar: Modularity of special cycles in orthogonal and unitary Shimura varieties
Speaker: Salim Tayou – Harvard University 3:00 PM-4:00 PM May 1, 2024 1 Oxford Street, Cambridge, MA 02138 USA
Since 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. ========================================= For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html - SEMINARS: Dynamics, Geometry and Moduli Spaces Seminar: Counting minimal surfaces in hyperbolic 3-manifolds
Speaker: Ruojing Jiang – MIT 4:00 PM-5:00 PM May 1, 2024 See webpage for more details: https://people.math.harvard.edu/~ctm/sem/ - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Toric Matroid Bundles
Speaker: Christopher Manon – University of Kentucky 4:15 PM-5:15 PM May 1, 2024
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. =============================== For more info, see https://math.mit.edu/combin/
| 2 - CMSA EVENT: Workshop on Global Categorical Symmetries
9:00 AM-5:00 PM May 2, 2024-May 3, 2024 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 EVENT: CMSA Active Matter Seminar: Control of parametric amplification in space-time modulated mechanical metamaterials
Speaker: Jayson Paulose – University of Oregon 1:30 PM-2:30 PM May 2, 2024
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 - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry
Speaker: Clay Còrdova – University of Chicago 2:00 PM-2:50 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 We 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/ - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: Symmetries, Invertible Field Theories, and Gauge Theory Phases
Speaker: Thomas Dumitrescu – UCLA 3:00 PM-3:50 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 I 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/ - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: The universal target category
Speaker: Theo Johnson-Freyd – Dalhousie University and Perimeter Institute 4:30 PM-5:20 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 Hilbert’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/
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26 | 27 | 28 | 29 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 29, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138 In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. The conference aims to actively engage and empower junior researchers and women, ensuring their integral presence and impactful contributions. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. - CMSA EVENT: Amplituhedra and Positive Geometry
9:00 AM-5:00 PM May 29, 2024-May 31, 2024 Amplituhedra and Positive Geometry May 29–31, 2024 Organizers: Further details TBA.
| 30 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 30, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138 In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. The conference aims to actively engage and empower junior researchers and women, ensuring their integral presence and impactful contributions. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. - CMSA EVENT: Amplituhedra and Positive Geometry
9:00 AM-5:00 PM May 30, 2024-May 31, 2024 Amplituhedra and Positive Geometry May 29–31, 2024 Organizers: Further details TBA.
| 31 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 31, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138 In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. The conference aims to actively engage and empower junior researchers and women, ensuring their integral presence and impactful contributions. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. - CMSA EVENT: Amplituhedra and Positive Geometry
9:00 AM-5:00 PM May 31, 2024-May 31, 2024 Amplituhedra and Positive Geometry May 29–31, 2024 Organizers: Further details TBA.
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