Calendar

**CANCELED**

Societal accumulation of knowledge is a complex, and arguably error-prone, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning, but also on the correctness of old units that the new one builds on. If left unchecked, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk, we describe our attempts to model such phenomena using probablistic models – we describe models for growth of cumulative knowledge, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model, when effects of errors may survive, and when they are totally eliminated.

The central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge), then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge, either of which would be overwhelming.

Based on the papers:

Is this correct? Let’s check!
Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, Madhu Sudan
arXiv:2211.12301

Errors are Robustly Tamed in Cumulative Knowledge Processes
Anna Brandenberger, Cassandra Marcussen, Elchanan Mossel, Madhu Sudan
arXiv:2309.05638

The eigenvalues of a uniformly distributed unitary matrix have the physical interpretation of a system of particles subject to a logarithmic pair interaction, restricted to lie on the unit circle and at inverse temperature 2. In this talk, I will present a more general model in which the unit circle is replaced by a sufficiently regular Jordan curve, at any positive temperature. I will show how to obtain the asymptotic partition function and Laplace transform of a linear statistic. These can be expressed using either the exterior conformal mapping of the curve or its associated Grunsky operator. Based on joint work with Kurt Johansson.

Abstract TBA

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar

Talk at 3 pm in Science Center 507; Tea at 4 pm in the Math Common Room

Please see website for more details: www.math.harvard.edu/~ctm/sem.

The derived category of a variety is an important and difficult invariant. In this talk, I discuss a purely convex-geometric and combinatorial approach to these categories for toric varieties. Along the way, we will run into the curious question of studying the contractibility of set differences of polytopes. I will focus on the toric variety of the permutahedron which has played an important role in many recent developments in matroid theory. I will discuss how this derived category can be described through the theory of matroids.

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For more info, see https://math.mit.edu/combin/

Materials that increase in size offer intriguing possibilities for shape morphing applications. Here, we explore two such systems—swelling polyacrylamide hydrogels and expanding polyurethane foams. The hydrogels swell by absorbing water into crosslinked polymer networks. They can therefore be modeled by coupling solvent migration with the deformations of a hyperelastic solid. In contrast, the foams initially behave as liquids with viscosity and volume increasing in time, responding elastically only when close to solidification. We investigate how these expanding materials are sculpted by complex environments with obstacles and trenches.

This seminar will be held in person and on Zoom.

https://harvard.zoom.us/j/96657833341

Password: cmsa

I will discuss the action induced by Adams operations on V times THH(\ell), where V is a type 2 complex.

Last summer, in this seminar, I introduced a dynamical system called “complex billiards” that extends the classical real billiards map to the setting of curves over algebraically closed fields. The dynamical degree of complex billiards is an invariant that describes the “algebraic entropy”, or chaos, of the system. In my previous talk, I proved an upper bound on this dynamical degree. In this talk, we derive lower bounds on the dynamical degree (a more challenging problem) through a careful study of one very special billiard table, the Fermat hyperbola. Independently of this result, we construct an algebraically stable model for complex billiards in the Fermat hyperbola using a little bit of complex dynamics. It is NOT necessary to have attended (or to remember) the previous talk, as I will begin again with all the key definitions.

Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information

In this talk, I’ll discuss the remarkable connections between the modular bootstrap and sphere packing or ground state problems discovered by Hartman, Mazáč, and Rastelli in 2019, with a focus on opportunities for further progress.

We investigate a minimal model of a nematopolar system. We analytically uncover a phase diagram consisting of a locked phase where the polar order and nematic order are locked, and unlocked phases which could be ordered or disordered. In particular, we develop two complementary perspectives on the locked phase: (i) the nematic order induces polar order, (ii) in the locked phase, all 1/2 integral nematic topological charges are confined. In particular, a polar +1 defect fattens from a point along a string with constant tension and confines a pair of nematic +1/2 defects at its ends.

Friday, Apr. 5th at 12pm, with lunch, lounge at CMSA (20 Garden Street).

Also by Zoom: https://harvard.zoom.us/j/92410768363

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

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For more info, see https://math.mit.edu/combin/

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

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For more info, see https://math.mit.edu/combin/