|
Sun | Mon | Tue | Wed | Thu | Fri | Sat |
---|
March | March | March | March | March | March | 1 |
2 | 3 - CMSA EVENT: CMSA Algebraic Geometry in String Theory: Kähler–Einstein metrics on families of Fano varieties
Speaker: Chung-Ming Pan – Institut de Mathématiques de Toulouse 10:00 AM-11:00 AM April 3, 2023
This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler–Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials.
This is joint work with Antonio Trusiani.
**Note special time & location: 10 – 11 AM ET in Room G02** https://cmsa.fas.harvard.edu/event/algebraic-geometry-in-string-theory/ - CMSA EVENT: CMSA Colloquium: Black hole microstate counting from the gravitational path integral
Speaker: Luca Iliesiu – Stanford University 11:00 AM-12:00 PM April 3, 2023 20 Garden Street, Cambridge, MA 02138
Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.
| 4 - SEMINARS: Mathematical Picture Language Seminar: The TTbar deformation of 2d quantum field theory and modular forms
Speaker: John Cardy – UC Berkeley and All Souls College, Oxford 9:30 AM-10:30 AM April 4, 2023
“TTbar” deformed 2d quantum field theory is a non-local theory in which Minkowski space is deformed in a state-dependent but consistent manner. For a massive theory this is equivalent to each particle acquiring a width proportional to its mass in its rest frame, giving rise to simple CDD factors dressing the $S$–matrix, but for deformed conformal field theories the spectrum becomes quite complicated, and the question of modular invariance of the torus partition function is non-trivial. I will show that this leads to a theory of TTbar deformed modular forms in general. Maass forms turn out to play an important role as eigenforms of the deformation.
The Math Picture Language seminar will be held at 9:30 a.m. Boston time. Click the link for a Zoom Link for Tuesday Math Picture Language Seminars. Recorded seminars can be viewed on the Mathematical Picture Language YouTube channel. - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Resonance and Koszul modules in algebraic geometry
Speaker: Gavril Farkas – Humboldt University 3:00 PM-4:00 PM April 4, 2023 1 Oxford Street, Cambridge, MA 02138 USA Inspired from ideas in topology, Koszul modules and the associated resonance varieties turned out to have important algebro-geometric applications for instance to (i) Green’s Conjecture on syzygies of canonical curves, (ii) stabilization of cohomology of projective varieties in arbitrary characteristics and (iii) Chen invariants of hyperplane arrangements. I will discuss new developments related to this circle of ideas obtained in joint work with Aprodu, Raicu and Suciu. - SEMINARS: Introductory Mathematics Seminar: Framing and Implementing Organizational Change in University Entry-Level Mathematics
Speaker: Deborah Moore-Russo – University of Oklahoma 4:30 PM-5:30 PM April 4, 2023 1 Oxford Street, Cambridge, MA 02138
Finding, applying and learning from the appropriate frameworks to use as lenses for educational research is an important task. In this talk I will share the three theoretical frameworks that I have used to study entry-level mathematics endeavors including: widespread change at a university (that involved implementation of TA training, course coordination, and many other efforts); leaders selected for funded efforts to incorporate active learning; and viability of mathematics tutoring centers. While I will give specific examples from my own research, each of the frameworks could be used to study a variety of university entities.
| 5 - NUMBER THEORY SEMINAR: Number Theory Seminar: Evaluating the wild Brauer group
Speaker: Rachel Newton – King’s College London 3:00 PM-4:00 PM April 5, 2023 1 Oxford Street, Cambridge, MA 02138 USA
The local global approach to the study of rational points over number fields begins by embedding the set of rational points on a variety X into the set of its adelic points. The Brauer-Manin pairing cuts out a subset of the adelic points, called the Brauer-Manin set, that contains the rational points. If the set of adelic points is non-empty but the Brauer–Manin set is empty then we say there’s a Brauer–Manin obstruction to the existence of rational points on X. Computing the Brauer–Manin pairing involves evaluating elements of the Brauer group of X at local points. If an element of the Brauer group has order coprime to p, then its evaluation at a p-adic point factors via reduction of the point modulo p. For elements of order a power of p this is no longer the case: in order to compute the evaluation map one must know the point to a higher p-adic precision. Classifying Brauer group elements according to the precision required to evaluate them at p-adic points gives a filtration which we describe using work of Kato. Applications of our work include addressing Swinnerton-Dyer’s question about which places can play a role in the Brauer–Manin obstruction. This is joint work with Martin Bright. - CMSA EVENT: CMSA Probability Seminar: Sampling from the SK and mixed p-spin measures with stochastic localization
Speaker: Ahmed El Alaoui – Cornell 3:30 PM-4:30 PM April 5, 2023 20 Garden Street, Cambridge, MA 02138
I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.
- HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Realizable Standard Young Tableaux
Speaker: Amanda Burcroff – Harvard 4:15 PM-5:15 PM April 5, 2023
We will discuss enumerative and structural properties of two families of standard Young tableaux, the realizable rectangular tableaux and the realizable staircase tableaux. The realizable rectangular tableaux come from tropical rank 1 matrices, whereas the realizability condition for staircase tableaux comes from geometric realizability for sorting networks and the Edelman-Greene bijection. The two notions of realizability are connected via the study of coherent monotone paths on the permutahedron, as established by Black and Sanyal in their study of flag polymatroids. As a consequence of providing tight asymptotic bounds on the size of these families, we make progress on the related studies of random sorting networks, realizable allowable sequences, and sorting algorithms. Based on joint work with Igor Araujo, Alexander E. Black, Yibo Gao, Robert A. Krueger, and Alex McDonough. ======================================================= For information about the Combinatorics Seminar, please visit… http://math.mit.edu/seminars/combin/ ============================================= - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: Sums of two cubes
Speaker: Levent Alpöge – Harvard 4:30 PM-5:30 PM April 5, 2023 1 Oxford Street, Cambridge, MA 02138 USA
I will connect the following questions and answers. 1. 42 = (12602123297335631)^3 + (80435758145817515)^3 + (-80538738812075974)^3. 2. https://people.math.harvard.edu/~alpoge/fun/fruit%20for%20thought.jpeg , aka: Are there positive integers x, y, z such that: x / (y + z) + y / (x + z) + z / (x + y) = 4? 3. The Birch and Swinnerton-Dyer conjecture. 4. Hilbert’s tenth problem, aka: Is there a computer program which “solves all Diophantine equations”? 5. 0% of integers are a sum of two squares (integral or rational). 6. A positive proportion of integers are a sum of two rational cubes.
For more information, please see: https://people.math.harvard.edu/~ana/ons/
| 6 - CMSA EVENT: CMSA General Relativity: Rough solutions of the relativistic Euler equations
Speaker: Sifan Yu – Vanderbilt University, Department of Mathematics 9:30 AM-10:30 AM April 6, 2023
I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework, . Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.
This seminar will be broadcast over Zoom: https://harvard.zoom.us/j/7855806609 - CMSA EVENT: Thursday Seminar: Gm-stabilization after Bachmann and Yakerson
Speaker: Elden Elmanto – Harvard 3:30 PM-5:30 PM April 6, 2023 1 Oxford Street, Cambridge, MA 02138 USA
I will prove that certain “motivic abelian groups” are motivic infinite loop spaces.
| 7 - CONFERENCE: Current Developments in Mathematics 2023
All day April 7, 2023-April 8, 2023 1 Oxford Street, Cambridge, MA 02138 USA Current Developments in Mathematics 2023April 7-8, 2023Harvard University Science CenterLecture Hall CSpeakers: Amol Aggarwal – Columbia University (Columbia) Bhargav Bhatt – Institute for Advanced Study, Princeton University, & University of Michigan (IAS/Princeton/UMichigan) Paul Bourgade – New York University, Courant Institute (NYU Courant) Vesselin Dimitrov – Institute for Advanced Study & Georgia Institute of Technology (IAS/Georgia Tech) Greta Panova – University of Southern California (USC) Register Here REQUESTS FOR FUNDING ARE CLOSED AS OF MARCH 10TH, 2023. Conference Schedule Download PDF for a detailed schedule of lectures and events. | |
---|
- 1:30 p.m. – 2:20 p.m. Part 1
- 2:20 p.m. – 2:30 p.m. Break
2:30 p.m. – 3:20 p.m. Part 2 Bhargav Bhatt $p$-adic motives | - 9:05 a.m. – 9:55 a.m. Part 1
- 9:55 a.m. – 10:05 a.m. Break
10:05 a.m. – 10:55 a.m. Part 2 Greta Panova Computational complexity in algebraic combinatorics | 3:20 p.m. – 3:35 p.m. Break | 10:55 a.m. – 11:10 a.m. Break | - 3:35 p.m. – 4:25 p.m. Part 1
- 4:25 p.m. – 4:35 p.m. Break
4:35 p.m. – 5:25 p.m. Part 2 Amol Aggarwal Universality results in random tiling models | - 11:10 a.m. – 12 p.m. Part 1
- 12 p.m. – 1:30 p.m. Lunch
1:30 p.m. – 2:20 p.m. Part 2 Paul Bourgade Random matrices, the Riemann zeta function and branching processes | | 2:20 p.m. – 2:35 p.m. Break | | - 2:35 p.m. – 3:25 p.m. Part 1
- 3:25 p.m. – 3:35 p.m. Break
3:35 p.m. – 4:25 p.m. Part 2 Vesselin Dimitrov Modular forms and arithmetic algebraization methods |
Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology. Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here. - CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Enhancing Detection of Topological Order by Local Error Correction
Speaker: Nishad Maskara – Harvard University 10:00 AM-11:30 AM April 7, 2023 20 Garden Street, Cambridge, MA 02138
The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.
This seminar offers the option to attend by Zoom. For information on how to join, please see:
- SEMINARS: Gauge Theory and Topology Seminar: Instantons on Joyce’s G2-manifolds
Speaker: Langte Ma – Stony Brook University 3:30 PM-4:30 PM April 7, 2023 1 Oxford Street, Cambridge, MA 02138 USA
As 7-manifolds with special holonomy, examples of compact G2-manifolds were first constructed by Joyce as resolutions of flat G2-orbifolds. Later Walpuski constructed non-trivial G2-instantons over Joyce’s manifolds via gluing techniques. In this talk, I will first explain how to define a deformation invariant of G2-orbifolds by counting flat connections, then describe the moduli space of instantons over certain non-compact G2-manifolds that appeared in Joyce’s construction, with the aim to give a complete description of moduli spaces over some examples in Joyce’s list.
| 8 - CONFERENCE: Current Developments in Mathematics 2023
All day April 8, 2023-April 8, 2023 1 Oxford Street, Cambridge, MA 02138 USA Current Developments in Mathematics 2023April 7-8, 2023Harvard University Science CenterLecture Hall CSpeakers: Amol Aggarwal – Columbia University (Columbia) Bhargav Bhatt – Institute for Advanced Study, Princeton University, & University of Michigan (IAS/Princeton/UMichigan) Paul Bourgade – New York University, Courant Institute (NYU Courant) Vesselin Dimitrov – Institute for Advanced Study & Georgia Institute of Technology (IAS/Georgia Tech) Greta Panova – University of Southern California (USC) Register Here REQUESTS FOR FUNDING ARE CLOSED AS OF MARCH 10TH, 2023. Conference Schedule Download PDF for a detailed schedule of lectures and events. | |
---|
- 1:30 p.m. – 2:20 p.m. Part 1
- 2:20 p.m. – 2:30 p.m. Break
2:30 p.m. – 3:20 p.m. Part 2 Bhargav Bhatt $p$-adic motives | - 9:05 a.m. – 9:55 a.m. Part 1
- 9:55 a.m. – 10:05 a.m. Break
10:05 a.m. – 10:55 a.m. Part 2 Greta Panova Computational complexity in algebraic combinatorics | 3:20 p.m. – 3:35 p.m. Break | 10:55 a.m. – 11:10 a.m. Break | - 3:35 p.m. – 4:25 p.m. Part 1
- 4:25 p.m. – 4:35 p.m. Break
4:35 p.m. – 5:25 p.m. Part 2 Amol Aggarwal Universality results in random tiling models | - 11:10 a.m. – 12 p.m. Part 1
- 12 p.m. – 1:30 p.m. Lunch
1:30 p.m. – 2:20 p.m. Part 2 Paul Bourgade Random matrices, the Riemann zeta function and branching processes | | 2:20 p.m. – 2:35 p.m. Break | | - 2:35 p.m. – 3:25 p.m. Part 1
- 3:25 p.m. – 3:35 p.m. Break
3:35 p.m. – 4:25 p.m. Part 2 Vesselin Dimitrov Modular forms and arithmetic algebraization methods |
Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology. Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.
|
9 | 10 - CMSA EVENT: CMSA Swampland Seminar: Swampland bounds on the abelian gauge sectors
Speaker: Seung-Joo Lee – IBS Daejeon 11:00 AM-12:00 PM April 10, 2023 20 Garden Street, Cambridge, MA 02138
In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk. - CMSA EVENT: CMSA Probability Seminar: Localization for random band matrices
Speaker: Ron Peled – Tel Aviv University 3:00 PM-4:00 PM April 10, 2023 20 Garden Street, Cambridge, MA 02138 **Note unusual day and time**
I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}. Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.
| 11 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Mirror symmetry, stability conditions, and geometric invariant theory
Speaker: Tristan Collins – MIT 3:00 PM-4:00 PM April 11, 2023
Bridgeland stability conditions were originally motivated by the concept of Pi stability in theoretical physics, as introduced in work of M. Douglas. Pi stability is an attempt to describe BPS states in string theory compactifications. Alternatively, BPS states in string theory can often be described by solutions of certain nonlinear partial differential equations. In this talk I will explain how, starting from nonlinear PDEs, ideas in GIT lead to a version of algebraic stability which is similar to Bridgeland stability. In particular, I will explain how in several examples in dimension 2, GIT stability for line bundles implies Bridgeland stability, but not conversely. In particular, this yields effective tests for Bridgeland stability in many examples.
| 12 - CMSA EVENT: CMSA Colloquium: Unexpected Uses of Neural Networks: Field Theory and Metric Flows
Speaker: James Halverson – Northeastern University 12:30 PM-1:30 PM April 12, 2023 20 Garden Street, Cambridge, MA 02138
We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows, such as Perelman’s formulation of Ricci flow, in particular limits.
- NUMBER THEORY SEMINAR: Number Theory Seminar: Square root p-adic L-functions
Speaker: Michael Harris – Columbia 3:00 PM-4:00 PM April 12, 2023 1 Oxford Street, Cambridge, MA 02138 USA
The Ichino–Ikeda conjecture, and its generalization to unitary groups by N. Harris, gives explicit formulas for central critical values of a large class of Rankin–Selberg tensor products. The version for unitary groups is now a theorem, and expresses the central critical value of L-functions of the form L(s, Π × Π′) in terms of squares of automorphic periods on unitary groups. Here Π×Π′ is an automorphic representation of GL(n, F) × GL(n − 1, F) that descends to an automorphic representation of U(V) × U(V′), where V and V′ are hermitian spaces over F, with respect to a Galois involution c of F, of dimension n and n − 1, respectively. I will report on the construction of a p-adic interpolation of the automorphic period — in other words, of the square root of the central values of the L-functions — when Π′ varies in a Hida family. The construction is based on the theory of p-adic differential operators due to Eischen, Fintzen, Mantovan, and Varma. Most aspects of the construction should generalize to higher Hida theory. I will explain the archimedean theory of the expected generalization, which is the subject of work in progress with Speh and Kobayashi. - CMSA EVENT: CMSA Probability Seminar: Large deviations of Selberg’s central limit theorem
Speaker: Emma Bailey – CUNY 3:30 PM-4:30 PM April 12, 2023 20 Garden Street, Cambridge, MA 02138
Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance. It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials. It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.
**location in Room G-10 is tentative. Posting will be updated with new location if necessary** - HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Vector bundles, valuations, tropical linear spaces and matriods
Speaker: Kiumars Kaveh – University of Pittsburgh 4:15 PM-5:15 PM April 12, 2023
Torus equivariant rank r vector bundles on a toric variety (toric vector bundles) were famously classified by Klyachko (1989) using certain combinatorial data of compatible filtrations in an r-dimensional vector space E. This data can be thought of as a higher rank generalization of an (integer-valued) piecewise linear function. In this talk, we give interpretations of Klyachko data in terms of valuations with values in a certain meet-join lattice as well as points on a tropical linear space. Since tropical linear spaces correspond to linear matroids, this point of view leads us to introduce the notion of a “matroidal vector bundle”, a generalization of toric vector bundles to general matroids (possibly non-representable). The talk focuses on the combinatorial side of the story and I will give a brief review of toric varieties at the beginning. This is a work in progress with Chris Manon (Kentucky). ======================================================= For information about the Combinatorics Seminar, please visit… http://math.mit.edu/seminars/combin/ =============================================
| 13 - CMSA EVENT: CMSA General Relativity Seminar: Resolving the photon ring
Speaker: Shahar Hadar – University of Haifa 9:30 AM-10:30 AM April 13, 2023
In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region, the photon shell, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.
This seminar will be broadcast over Zoom: https://harvard.zoom.us/j/98794872462 - CMSA EVENT: CMSA Active Matter: Control of actin cable length by decelerated growth and network geometry
Speaker: Shane McInally – Brandeis University 1:00 PM-2:00 PM April 13, 2023 20 Garden Street, Cambridge, MA 02138
The sizes of many subcellular structures are coordinated with cell size to ensure that these structures meet the functional demands of the cell. In eukaryotic cells, these subcellular structures are often membrane-bound organelles, whose volume is the physiologically important aspect of their size. Scaling organelle volume with cell volume can be explained by limiting pool mechanisms, wherein a constant concentration of molecular building blocks enables subcellular structures to increase in size proportionally with cell volume. However, limiting pool mechanisms cannot explain how the size of linear subcellular structures, such as cytoskeletal filaments, scale with the linear dimensions of the cell. Recently, we discovered that the length of actin cables in budding yeast (used for intracellular transport) precisely matches the length of the cell in which they are assembled. Using mathematical modeling and quantitative imaging of actin cable growth dynamics, we found that as the actin cables grow longer, their extension rates slow (or decelerate), enabling cable length to match cell length. Importantly, this deceleration behavior is cell-length dependent, allowing cables in longer cells to grow faster, and therefore reach a longer length before growth stops at the back of the cell. In addition, we have unexpectedly found that cable length is specified by cable shape. Our imaging analysis reveals that cables progressively taper as they extend from the bud neck into the mother cell, and further, this tapering scales with cell length. Integrating observations made for tapering actin networks in other systems, we have developed a novel mathematical model for cable length control that recapitulates our quantitative experimental observations. Unlike other models of size control, this model does not require length-dependent rates of assembly or disassembly. Instead, feedback control over the length of the cable is an emergent property due to the cross-linked and bundled architecture of the actin filaments within the cable. This work reveals a new strategy that cells use to coordinate the size of their internal parts with their linear dimensions. Similar design principles may control the size and scaling of other subcellular structures whose physiologically important dimension is their length.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/ - THURSDAY SEMINAR SEMINAR: Thursday Seminar: Real-etale localization
Speaker: Lucy Yang – Harvard 3:30 PM-5:30 PM April 13, 2023 1 Oxford Street, Cambridge, MA 02138 USA No additional detail for this event.
| 14 - CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries
Speaker: Guanyu Zhu – IBM Quantum, T. J. Watson Research Center 10:00 AM-11:30 AM April 14, 2023 20 Garden Street, Cambridge, MA 02138
Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects. References: 1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua 2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O'Connor, Guanyu Zhu 3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhus.
This seminar offers the option to attend by Zoom. For information on how to join, please see:
- SEMINARS: Gauge Theory and Topology Seminar: Lattice Floer Spectra
Speaker: Matthew Stoffregen – Michigan State University 3:30 PM-4:30 PM April 14, 2023 1 Oxford Street, Cambridge, MA 02138 USA
We calculate the monopole Floer spectra of almost-rational plumbings, including all Seifert-fibered rational homology spheres, following ideas from lattice homology. We’ll also talk about a key ingredient, an exact triangle for monopole Floer spectra. This is joint work with Irving Dai and Hirofumi Sasahira.
| 15 |
16 | 17 | 18 - SEMINARS: Mathematical Picture Language Seminar: Constructing algebraic quantum field theory
Speaker: Klaus Fredenhagen, II – Institut für Theoretische Physik, Universität Hamburg 9:30 AM-10:30 AM April 18, 2023 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard/MIT Algebraic Geometry Seminar: A canonical algebraic cycle associated to a curve in its Jacobian
Speaker: Padma Srinivasan – ICERM 3:00 PM-4:00 PM April 18, 2023 1 Oxford Street, Cambridge, MA 02138 USA
We will talk about the Ceresa class, which is the image under a cycle class map of a canonical homologically trivial algebraic cycle associated to a curve in its Jacobian. In his 1983 thesis, Ceresa showed that the generic curve of genus at least 3 has nonvanishing Ceresa cycle modulo algebraic equivalence. Strategies for proving Fermat curves have infinite order Ceresa cycles due to B. Harris, Bloch, Bertolini-Darmon-Prasanna, Eskandari-Murty use a variety of ideas ranging from computation of explicit iterated period integrals, special values of p-adic L functions and points of infinite order on the Jacobian of Fermat curves. In fact, Bloch’s results about the Ceresa cycle of Fermat quartics provided the first concrete evidence for the generalization of the BSD conjecture to the Bloch-Beilinson conjectures. We will survey several recent results about the Ceresa cycle and the Ceresa class. The Ceresa class vanishes for all hyperelliptic curves and was expected to be nonvanishing for non-hyperelliptic curves. We will present joint work with Dean Bisogno, Wanlin Li and Daniel Litt, where we construct a non-hyperelliptic genus 3 quotient of the Fricke–Macbeath curve with torsion Ceresa class, using the character theory of the automorphism group of the curve, namely, PSL2(F8). .
| 19 - NUMBER THEORY SEMINAR: Number Theory Seminar: Derived cycles on Shimura varieties
Speaker: Keerthi Madapusi – Boston College 3:00 PM-4:00 PM April 19, 2023 1 Oxford Street, Cambridge, MA 02138 USA
I will show how methods from derived algebraic geometry can be used to give a uniform definition of generating series of cycles on integral models of Shimura varieties of Hodge or even abelian type. Following conjectures of Kudla, these series are expected to converge to half-integer weight automorphic forms on split unitary groups, and certain ‘easy’ consequences of this expectation turn out to be indeed easy given the derived perspective. - CMSA EVENT: CMSA Probability Seminar: Diagonalizing Transition Matrices of Card shuffles
Speaker: Evita Nestoridi – Stony Brook University 3:30 PM-4:30 PM April 19, 2023
In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.
- HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Horizontal-strip LLT polynomials
Speaker: Foster Tom – MIT 4:15 PM-5:15 PM April 19, 2023
Lascoux, Leclerc, and Thibon defined a remarkable family of symmetric functions that are $q$-deformations of products of skew Schur functions. These LLT polynomials $G_{\lambda}(x;q)$ can be indexed by a tuple $\lambda$ of skew diagrams. When each skew diagram is a row, we define a weighted graph $\Pi(\lambda)$. We show that a horizontal-strip LLT polynomial is determined by this weighted graph. When $\Pi(\lambda)$ has no triangles, we establish a combinatorial Schur expansion of $G_{\lambda}(x;q)$. We also explore a connection to extended chromatic symmetric functions. ======================================================= For information about the Combinatorics Seminar, please visit: http://math.mit.edu/seminars/combin/ ============================================= - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: Illustrating infinity
Speaker: Curtis McMullen – Harvard University 4:30 PM-5:30 PM April 19, 2023 1 Oxford Street, Cambridge, MA 02138 USA What do you picture when you think of exp(z), a group of 2×2 matrices, a smooth map, or infinity itself? In this talk we will discuss the practice of mathematical illustration, and give a glimpse of some of the mathematics behind the posters on the first floor of the Science Center.
For more information, please see: https://people.math.harvard.edu/~ana/ons/
| 20 | 21 - CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order
Speaker: Subir Sachdev – Harvard 10:00 AM-11:30 AM April 21, 2023 20 Garden Street, Cambridge, MA 02138
Soon after the discovery of high temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid, and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram. As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885
This seminar offers the option to attend by Zoom. For information on how to join, please see:
- SEMINARS: Gauge Theory and Topology Seminar: The Dehn surgery characterisation of Whitehead doubles
Speaker: Laura Wakelin – Imperial College London 3:30 PM-4:30 PM April 21, 2023 1 Oxford Street, Cambridge, MA 02138 USA
A slope p/q is said to be characterising for a knot K if the oriented homeomorphism type of the manifold obtained by performing Dehn surgery of slope p/q on K uniquely determines the knot K. In this talk, I will discuss how JSJ decompositions and hyperbolic techniques can be used to find characterising slopes for a special class of satellite knots which includes Whitehead doubles. I will also exhibit a family of pairs of satellite knots sharing a non-characterising slope of the form 1/q. - HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Set-valued tableaux and enumeration of special chip configurations on graphs
Speaker: Nathan Pflueger – Amherst College 4:15 PM-5:15 PM April 21, 2023
Chip-firing games on finite graphs provide a combinatorial analog of the theory of special divisors on algebraic curves. Each chip configuration determines two numbers: the degree and rank, analogous to the degree and dimension of a linear series on an algebraic curve. I will consider the enumerative problem: on a given finite graph, how many classes of chip configuration are there of a given degree and rank? I will state a complete solution to this problem in the case of a famous example—the “chains of loops” studied by Cools, Draisma, Payne, and Robeva. The solution has an intriguing form: it is a symmetric polynomial, with coefficients given by counting set-valued Young tableaux, evaluated on the lengths of the loops. I will discuss some intriguing parallels to algebraic geometry, in which the same set-valued tableaux arise in the cohomology class and Euler characteristic of Brill-Noether varieties, and speculate on potential generalizations to other families of graphs and to motives of Brill-Noether varieties. ======================================================= For information about the Combinatorics Seminar, please visit: http://math.mit.edu/seminars/combin/ =============================================
| 22 |
23 | 24 - CMSA EVENT: CMSA Swampland Seminar: The Tameness of Quantum Field Theories
Speaker: Thomas Grimm – Utrecht University 11:00 AM-12:00 PM April 24, 2023 17 Oxford St, Cambridge, MA 02138
Tameness is a generalized notion of finiteness that is restricting the geometric complexity of sets and functions. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. In this talk I formalize the connection between quantum field theories and logical structures and argue that the tameness of a quantum field theory relies on its UV definition. I quantify our expectations on the tameness of effective theories that can be coupled to quantum gravity and on CFTs. In particular, I present tameness conjectures about CFT observables and propose universal constraints that render spaces of CFTs to be tame sets. I then highlight the relation of these conjectures to other swampland conjectures, e.g., by arguing that the tameness of CFT observables restricts having parametrical gaps in the operator spectrum.
| 25 - SEMINARS: Mathematical Picture Language Seminar: Amenability and von Neumann algebras
Speaker: Jesse Peterson – Vanderbilt University 9:30 AM-10:30 AM April 25, 2023 Amenability for groups is a concept that was first introduced by von Neumann in 1929 to provide an explanation of the Banach-Tarski paradox. The concept has since been exported to many different areas of mathematics and continues to hold an important position in fields such as group theory, ergodic theory, and operator algebras. In the area of von Neumann algebras, which von Neumann introduced a year later in 1930, the concept plays a fundamental role, and the classification of amenable von Neumann algebras by Connes and Haagerup is considered a touchstone of the field. In this talk, I will give a survey of amenability in von Neumann algebras, with special emphasis on recent uses of the concept and highlighting some of my own contributions.
The Math Picture Language seminar will be held at 9:30 a.m. Boston time. Click the link for a Zoom Link for Tuesday Math Picture Language Seminars. Recorded seminars can be viewed on the Mathematical Picture Language YouTube channel. - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Counting differentials with fixed residues
Speaker: Dawei Chen – Boston College 3:00 PM-4:00 PM April 25, 2023 1 Oxford Street, Cambridge, MA 02138 USA
In this talk, we investigate meromorphic differentials on the Riemann sphere with a single zero and several poles of predetermined orders. Our aim is to determine the number of such differentials that satisfy the condition where the residue at each pole is fixed. This question was previously explored by Gendron and Tahar, who employed graph counting techniques derived from the flat geometry of differentials. We introduce a new approach using intersection theory on moduli spaces of differentials. This is joint work with Miguel Prado Godoy.
https://sites.google.com/view/harvardmitag
| 26 - CMSA EVENT: CMSA Colloquium: Boundary behavior at classical and quantum phase transitions
Speaker: Max Metlitski – MIT 12:30 PM-1:30 PM April 26, 2023
There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions.
- HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Height moduli on algebraic stacks and counting families of varieties
Speaker: Jun-Yong Park – University of Melbourne 1:30 PM-2:30 PM April 26, 2023 **Note special day, time & location**
I will begin by reviewing the classical algorithm of Tate with some explicit polynomial calculations. Combining this with twisted stable maps theory leads us to the height moduli of rational points of fixed stacky height on the fine modular curve Mbar_{1,1} over global function fields. We will then compute arithmetic invariants of elliptic surfaces moduli via topological methods and give applications to counting elliptic curves over Fq(t).
https://sites.google.com/view/harvardmitag - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Toolformer: Language Models Can Teach Themselves to Use Tools
Speaker: Timo Schick – Meta AI 2:00 PM-3:00 PM April 26, 2023
Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions, especially at scale. They also, paradoxically, struggle with basic functionality, such as arithmetic or factual lookup, where much simpler and smaller models excel. In this talk, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer, a model trained to independently decide which APIs to call, when to call them, what arguments to pass, and how to best incorporate the results into future token prediction. Through this, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities.
This seminar will be on Zoom: - NUMBER THEORY SEMINAR: Number Theory Seminar: Knots Invariants and Arithmetic Statistics
Speaker: Tomer Schlank – Hebrew University of Jerusalem 3:00 PM-4:00 PM April 26, 2023 1 Oxford Street, Cambridge, MA 02138 USA - HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Resonance schemes and Hilbert series for Koszul modules
Speaker: Alex Suciu – Northeastern 4:15 PM-5:15 PM April 26, 2023
The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric settings. I will describe several conditions that ensure the reducedness of the associated projective resonance schemes and yield asymptotic formulas for the Hilbert series of the corresponding Koszul modules. For the exterior Stanley–Reisner rings of simplicial complexes, this approach leads to a relationship between resonance and Hilbert series that generalizes a known formula for the Chen ranks of a right-angled Artin groups. Based on joint work with Marian Aprodu, Gavril Farkas, Claudiu Raicu, and Alessio Sammartano. ======================================================= For information about the Combinatorics Seminar, please visit: http://math.mit.edu/seminars/combin/ =============================================
| 27 - CMSA EVENT: CMSA General Relativity Seminar: The localized seed-to-solution method for the Einstein constraints
Speaker: Philippe G. LeFloch – Sorbonne University and CNRS 10:30 AM-11:30 AM April 27, 2023
I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of `asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.
Zoom: https://harvard.zoom.us/j/7855806609 - CMSA EVENT: CMSA Active Matter Seminar: Competition at the front of expanding populations
Speaker: Mehran Kardar – MIT 1:00 PM-2:00 PM April 27, 2023 20 Garden Street, Cambridge, MA 02138
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/ - THURSDAY SEMINAR SEMINAR: Thursday Seminar: Proof of the motivic Freudenthal Suspension Theorem
Speaker: Mike Hopkins – Harvard 3:30 PM-5:30 PM April 27, 2023 1 Oxford Street, Cambridge, MA 02138 USA
It’s been a long trek. In this talk I will put the pieces back together and explain the proof of the motivic Freudenthal suspension theorem. - SEMINARS: Algebraic Dynamics Seminar: Marked cycle curves for quadratic polynomials and rational maps
Speaker: Giulio Tiozzo – University of Toronto 3:30 PM-5:30 PM April 27, 2023 We consider the algebraic curves obtained by marking a cycle of fixed period p in the space of quadratic polynomials. For each period, we produce a cell decomposition, whose combinatorics is closely related to the combinatorics of primitive components in the Mandelbrot set. This opens up many questions about their combinatorial and geometric structure. We also consider similar curves for the space of quadratic rational maps with a critical 2-cycle. Joint work with Caroline Davis, Malavika Mukundan, and Danny Stoll.
For more information, please see: Algebraic Dynamics Seminar at Harvard
**please note change in time and location**
| 28 - OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: Finding Balance in Chaos: Approximating orthogonal polynomials on Julia sets
Speaker: Madison Shirazi – Harvard Class of 2023 9:45 AM-10:15 AM April 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Equilibrium measures of compact sets in two dimensions are a generalization of equilibrium charge distributions on perfect conductors. Using equilibrium measures, we can compute the capacity of a compact set: the ability of the set to hold energy. We will compare two methods of approximating these equilibrium measures and thus the capacity of sets using finite collections of points, and then study the convergence behavior and properties of these approximations. - CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Fracton Self-Statistics
Speaker: Hao Song – ITP-CAS 10:00 AM-11:30 AM April 28, 2023
Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins. References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.
This seminar will be virtual. Password: cmsa For more information, please see:
- OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: Mostow rigidity and hyperbolic 3-manifolds
Speaker: Benjy Firester – Harvard Class of 2023 10:20 AM-10:50 AM April 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA
My thesis develops the theory of hyperbolic manifolds and explains two proofs of the foundational Mostow rigidity theorem. Great math theorems bridge fields, enabling us to transfer tools from one to another, exhibiting overarching themes that unify mathematics. Mostow rigidity is such a theorem. It proves the uniqueness of geometric structures on spaces of dimension at least three, demonstrating a deep connection between topology and geometry. Most 3-dimensional spaces are hyperbolic, meaning “negatively curved” like a hyperboloid. Understanding hyperbolic spaces is important to topology, algebra, dynamics, and more. This theory is critical to the geometrization theorem, perhaps the most celebrated result in geometry. Mostow rigidity shows that any homotopy equivalence between two hyperbolic manifolds, a topological relationship, can be uniquely deformed to an isometry, a geometric one. Mostow’s own proof uses quasi-conformal theory to improve an initial function only preserves the topological structure into one that preserves the geometric structure, linking the two notions of equivalence. The second proof defines a topological quantity capturing a manifold’s complexity, and computes the volume for hyperbolic manifolds. The algebraic realization of a hyperbolic manifold encodes the geometric data of which simplices (higher-dimensional triangles) have maximal volume, which are rigid above dimension two. - OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: From triangles to algebraic geometry
Speaker: Dori Bejleri – Harvard University 2:00 PM-2:45 PM April 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA
The classification of shapes is one of the central pursuits of geometry. In this talk, we will begin with the problem of classifying triangles and see how it leads naturally to the notion of moduli spaces in algebraic geometry. - HARVARD-MIT COMBINATORICS SEMINAR: MIT-Harvard-MSR Combinatorics Seminar: Equiangular lines and large multiplicity of fixed second eigenvalue
Speaker: Carl Schildkraut – MIT 3:00 PM-4:00 PM April 28, 2023
Given a fixed angle alpha and growing dimension n, what is the maximum number of lines in n dimensions, all pairs of which meet at the same angle alpha? In 2019, Jiang, Tidor, Yao, Zhang, and Zhao determined this to be n + o(n) for “most” angles alpha, and determined the answer within O(1) for the others; the main technical portion was a sublinear upper bound on the multiplicity of the second-largest eigenvalue of bounded degree graphs. We present two constructions of bounded degree graphs with second-largest eigenvalue of large multiplicity. The first gives multiplicity about n^(1/2) using group-theoretic techniques. The second gives multiplicity only log log n, but allows precise control on the value of the second eigenvalue. This corresponds to families of n + log log n equiangular lines with the same fixed angle alpha. For some values of alpha, this answers a question of Jiang and Polyanskii, as well as Jiang, Tidor, Yao, Zhang, and Zhao, in the negative. Partially based on joint work with Milan Haiman, Shengtong Zhang, and Yufei Zhao. ======================================================= For information about the Combinatorics Seminar, please visit: http://math.mit.edu/seminars/combin/ ============================================= - OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: When do varieties map to each other?
Speaker: Mihnea Popa – Harvard University 3:15 PM-4:00 PM April 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Algebraic geometers study algebraic varieties, and the maps between them. A basic question is whether there can be any non-constant maps between two (smooth, projective) varieties of different type. I will explain some basic and some more sophisticated obstructions to the existence of such maps.
| 29 |
30 | May | May | May | May | May | May |