# AdIMOM

## Adequate Institute of Mediocre and Outstanding Mathematics

About us |
Past Seminars |
**Conference**

On May 9 - 10, approximately twenty of us will gather online and spend the weekend talking about mathematics. We expect there to be nine talks over Saturday and Sunday. We will live video of food, coffee, tea and snacks in rich abundance, with a live scone-baking demonstration you are all invited to follow. If you share our philosophy and passion for mathematics, you are invited to join us for our fourth conference at AdIMOM.

For questions please email homemadeseminar [at] gmail [dot] com

In preparation for the lecture on scones, please assemble the following ingredients .

LINK TO VIDEO CALL

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Zoom meeting ID:99099974678

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Previous conferences

2019 conference

2018 conference

2017 conference

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Invited Speakers

- Ben Briggs,
*(University of Utah and AdIMOM)*
- Eduard Duriev,
*(Institut de mathematiques de Jussieu and AdIMOM)*
- Balazs Elek,
*(University of Toronto)*
- Özgür Esentepe,
*(University of Connecticut and AdIMOM)*
- Ehsaan Hossain,
*(University of Waterloo)*
- Anton Izosimov,
*(The University of Arizona)*
- Hannah Keese,
*(Cornell University)*
- Leonid Monin,
*(University of Bristol and AdIMOM)*
- Nikita Klemyatin,
*(National Research University Higher School of Economics and Skoltech)*

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Schedule (with further details about Sunday to come soon)

#### Abstracts

**Speaker**: Ben Briggs

**Date**: May 9, 2020

**Title**: How to recognise Complete intersection maps Categorically

**Abstract**:

I'll talk about how

Derived categories work

And all that yoga

Then I will explain

How complete intersections

Work with this structure

One consequence is

Avramovs theorem about

Factoring C.I.s

**Speaker**: Özgür Esentepe

**Date**: May 9, 2020

**Title**: Happel's theorem

**Abstract**: In the first half of this talk, I will talk about two different notions of Cohen-Macaulay modules over an order (a Cohen-Macaulay algebra) over a Cohen-Macaulay local ring. The special case where these two notions coincide is the case of Gorenstein orders. Gorenstein orders are akin to self-injective algebras in that they -as a module over themselves- are injective objects in the category of maximal Cohen-Macaulay modules. In the second half of this talk, I will talk about a theorem of Happel which says that the bounded derived category of a self-injective algebra of finite global dimension is triangle equivalent to stable category of graded modules over its trivial extension algebra. I will try to convince you that this theorem holds for orders of finite global dimension over Cohen-Macaulay local rings, as well, if one looks at the stable category of maximal Cohen-Macaulay modules over the trivial extension order.

**Speaker**: Nikita Klemyatin

**Date**: May 10, 2020

**Title**: Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group

**Abstract**: In the theory of differential manifolds one can prove the following fact: for any manifold M with an action of connected Lie group G the induced action on de Rham cohomology groups is trivial. However, this is not true for complex manifolds and Dolbeult cohomology groups, even the action of the Lie group is holomorphic. However, we can prove the similar fact for hermitian manifolds, if we add some very mild assumptions. More precisely, let G be a complex Lie group acting on a compact complex Hermitian manifold M by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.

**Speaker**: Leonid Monin

**Date**: May 9, 2020

**Title**: Inversion of matrices, C^* action on Grassmanian and the space of complete quadrics.

**Abstract**:In my talk I will explain how to invert a matrix using a torus action on Grassmanian and how all of this is related to the classical enumerative problems about quadrics in P^n.

**Speaker**: Anton Izosimov

**Date**: May 9, 2020

**Title**: The pentagram map and Poncelet polygons

**Abstract**: Let P be a planar pentagon, and let P' be the pentagon whose vertices are the intersection points of diagonals of P. Then a classical result due to Clebsch says that P and P' are projectively equivalent (i.e. there is a projective transformation taking P to P').
In 2007, R. Schwartz generalized this result to Poncelet polygons, i.e. polygons which are simultaneously inscribed in a conic and circumscribed about another conic (clearly, any pentagon has this property, so Poncelet polygons can be regarded as "generalized pentagons"). Namely, Schwartz proved that if P is a Poncelet polygon with odd number of vertices, and P' is the polygon whose vertices are the intersection points of shortest diagonals of P (i.e. diagonals connecting second nearest vertices), then P and P' are projectively equivalent.
In the talk, I will argue that in the convex case this property characterizes Poncelet polygons. In other words, if P is a convex odd-gon which is projectively equivalent to its “diagonal” polygon P', then P (and hence P') is a Poncelet polygon. The proof is based on the theory of commuting difference operators, as well as on properties of real elliptic curves and theta functions.

**Speaker**: Hannah Keese

**Date**: May 9, 2020

**Title**: Variations on a theme of Schubert

**Abstract**: In 1879, Hermann Schubert published the celebrated "Kalkül der abzählenden Geometrie" ("Calculus of Enumerative Geometry"), wherein he considered questions of the following form: "How many geometric objects of a given type fulfil certain given conditions?" For example: how many lines intersect four given general lines in (projective) 3-space? The method used to solve this counting problem and others like it in enumerative geometry is known as Schubert calculus. I will begin with the theme: a historical look at Schubert Calculus As Schubert Did It, before moving on to more modern variations of the calculus, potentially explaining why the number 5 819 539 783 680 is interesting along the way.

**Speaker**: Eduard Duriev

**Date**: May 10, 2020

**Title**: Counting meanders, ribbons and squares on surfaces

**Abstract**: TBA

**Speaker**: Ehsaan Hossain

**Date**: May 10, 2020

**Title**: Large Recurrence in Algebraic Dynamics

**Abstract**: Define a recursive orbit $z_n := \varphi_c(z_{n-1})$ with $z_0=0$, where $\varphi_c(z)=z^2+c$ is a ``generic'' quadratic over a field of characteristic zero. How often is $z_n=0$? This is the $1$-dimensional, quadratic version of the far-reaching Dynamical Mordell--Lang Problem, which states that if $z_n=0$ for infinitely many $n$, then $z_n=0$ periodically. So for example, you can't have $z_n=0$ iff $n$ is prime --- that would be ludicrous! This problem has exciting resolutions in higher-dimensional cases, \textit{e.g.} orbits of surface endomorphisms, or automorphisms of any variety. But DML is still open in its full generality. We present a solution when $z_n=0$ for ``too many'' $n$, where ``too many'' is interpreted in various Ramsey-theoretic senses. This will lead us down the rabbit hole of ergodic theory, ultrafilters, and the wonderful Poincar\'{e} Recurrence Theorem.

**Speaker**: Balazs Elek

**Date**: May 10, 2020

**Title**: The Borel Fixed Point Theorem and some applications

**Abstract**: The Borel Fixed Point Theorem says that a solvable group acting on a proper variety has a fixed point. After explaining what these words mean and proving the theorem, we will explore some applications in geometry and representation theory.