Seminario Conexión de GALoiS - 1.3.24 - John Alexander CRUZ - Can a mirror map be seen as a covering map?

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Andrés Villaveces

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Feb 28, 2024, 2:56:26 PMFeb 28
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber
Friday, March 1st, 12:00 to 13:30 Chicago time

OJO: 13:00 a 14:30 Hora de Bogotá


John Alexander CRUZ (UNAL)

Can a mirror map be seen as a covering map?

Abstract: I will try to argue that a general mirror map can be seen as a covering map from the fact that it satisfies certain differential equation. If my argument works then this should help to use Zilber's program and Freitag-Nagloo program (related to their work with Blázquez-Sanz and Casale) in order to understand mirror maps from a model theoretic point of view.

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Andrés Villaveces

avillavecesn.net
Departamento de Matemáticas - Edificio 404
Universidad Nacional de Colombia
AK 30 # 45-03
111321 - Bogotá - Colombia
Tel: +57 601 3165000 ext 13209

Andrés Villaveces

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Mar 6, 2024, 12:38:25 PMMar 6
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber, Gustavo Cipagauta
Friday, March 8, 12:00 to 13:30 Chicago time

OJO: 13:00 a 14:30 Hora de Bogotá

 
John Alexander CRUZ (UNAL)

Can a mirror map be seen as a covering map? (2)

Abstract: I will try to argue that a general mirror map can be seen as a covering map from the fact that it satisfies a certain differential equation. If my argument works then this should help to use Zilber's program and Freitag-Nagloo program (related to their work with Blázquez-Sanz and Casale) in order to understand mirror maps from a model theoretic point of view.

Note: the recording of Alex's first session [notably, his coloquy with Zilber and Libgober toward the end of the session] is available on the website of the seminar (link below).

Andrés Villaveces

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Mar 13, 2024, 10:30:46 PMMar 13
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber, Gustavo Cipagauta
Friday, March 15, 12:00 to 13:30 Chicago and Bogotá time

OJO: a partir de esta semana el seminario es a las 12:00 en Bogotá


John Alexander CRUZ (UNAL)

Can a mirror map be seen as a covering map? (III) + Synthesis Session


Alex Cruz will close his series started this month with further discussion on the questions that have arisen. We will all have an open discussion on possibilities, lines of research, etc. on model theoretic approaches to the understanding of mirror maps.

Andrés Villaveces

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Apr 2, 2024, 6:09:30 PMApr 2
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber, Gustavo Cipagauta, Juan Nido
Friday, 5 April, 12:00 to 13:30 Chicago and Bogotá time. 18:00 Oxford - 17:00 GMT
 

Boris ZILBER - University of Oxford


Definability of topological invariants and some thoughts on mirror symmetry


Abstract: I am going to explain how categorical $L_{\omega_1,\omega}$-theory of cover of a complex variety X can be seen as a complete topological invariant of X.

A further analysis of the axioms reveals two quite different subtheories - one describing the Zariski/holomorphic components of the structure and another - the discrete/metric components.

This suggests an interplay of two distinct geometric categories, similar to the ones conjectured by Kontsevich's HMS.

Andrés Villaveces

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Apr 10, 2024, 11:13:56 PMApr 10
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber, Gustavo Cipagauta, Juan Nido
Friday, 12 April, 12:00 to 13:30 Chicago and Bogotá time - 17:00 GMT
 

Anatoly LIBGOBER - University of Illinois at Chicago


Problems in the study of infinite degree covers in algebraic geometry


Abstract: I will discuss natural algebro-geometric constructions which lead to infinite degree covers of algebraic varieties including universal covers and period maps as well as some classical conjectures about their structure.


I also discuss how works of Lian-Yau and C.Doran on automorphic and integrality properties of mirror maps fit into this circle of questions.

Andrés Villaveces

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Apr 17, 2024, 12:02:48 PMApr 17
to logbog, John Baldwin, John Alexander Cruz Morales, coocurm...@unal.edu.co, Leonardo Arturo Cano Garcia, David Blazquez Sanz, Joel Nagloo, Zoran Skoda, Xavier Caicedo, Anatoly Libgober, Departamento de Matem�ticas Ciencias, Michael Harris, Boris Zilber, Gustavo Cipagauta, Juan Nido
Friday, 19 April, 12:00 to 13:30 Chicago and Bogotá time - 17:00 GMT
 

James FREITAG - University of Illinois at Chicago


Examples of differential equations arising from the action of a discrete group


Abstract: Abstract: Mainly, I'd like to talk about examples of differential equations arising from the action of a discrete group. The main issue I'd like to expose is how o-minimality plays a role. Part of the talk will be about equations on moduli spaces, and part will be about a new look at Manin kernels from this perspective.
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