Calendar

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363

Zoom: https://harvard.zoom.us/j/7855806609

Password: cmsa

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363

We call a function f linear if f(x+y) = f(x) + f(y) holds for all x,y. It is natural to call f “99% linear” if instead, this identity holds for most pairs (x,y); say, 99% of
pairs. Similarly, we could say f is “1% linear” if this identity holds 1% of the time. A natural question is then: what can we say about the structure of “99% linear” or “1% linear” functions? Are they always just perturbations of true 100% linear functions, or are there other examples?

Given almost any algebraic definition, you can similarly ask about its approximate variants, and if you can prove a strong positive statement, it tends to have applications. In particular, I will discuss how 1% linear functions relate to the Polynomial Freiman-Ruzsa conjecture, and how 1% polynomial functions relate to the Inverse Theorem for the Gowers norms.

Zoom QR Code & Link:
https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
Passcode: 657361
https://mathpicture.fas.harvard.edu/seminar

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363

See webpage for more details: https://people.math.harvard.edu/~ctm/sem/

The multispecies ASEP (mASEP) is a Markov chain in which particles of different species hop on a one-dimensional lattice. The doubly ASEP (DASEP) is like the mASEP, but it additionally allows spontaneous change of species. We will introduce two new Markov chains that the DASEP lumps to, which give relations between sums of steady state probabilities. We also give explicit formulas for the stationary distribution of a particular infinite family.

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

Billiards is one of the most-studied dynamical systems, modeling the behavior of a point particle bouncing around some space. If the space is a plane region bounded by an algebraic curve, then we may use techniques from algebraic geometry to study its billiards map. We explain how to view billiards as a complex algebraic correspondence, and we prove upper and lower bounds on the dynamical degree, the growth rate of the degrees of the iterates, in terms of the degree of the boundary curve. These degree growth rates are studied in mathematical physics, broadly speaking, as a way to identify integrable (exactly solvable) physical models. In our setting, this theory gives us an upper bound on the entropy, or chaos, of billiards in curves.

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363

This semester we will go through the work of Burklund, Hahn, Levy and Schlank on the construction of counterexamples to the telescope conjecture.

Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.

Friday, Feb. 2nd at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363