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Mini Course
Speaker:
 Francois Charette (University of Ottawa, Canada)
Title: Lagrangian Quantum Homology with Applications to Symplectic Rigidity
Description:

 Lagrangian quantum homology was introduced by Biran and Cornea, as a tool to study Lagrangian submanifolds of symplectic manifolds. I will present an overview of its construction and give applications to Hamiltonian dynamics, open Gromov Witten invariants and rigidity of the Maslov class. The lecture assumes some familiarity with symplectic manifolds and Lagrangian submanifolds. Other notions will be introduced along the way, depending on the audience previous knowledge.

References for further reading:

  • Biran-Cornea have many papers on QH(L):
- A Lagrangian quantum homology,
- Rigidity and uniruling for Lagrangian submanifolds,
- Lagrangian topology and enumerative geometry,
  • For homological mirror symmetry:
Nick Sheridan, On the Fukaya category of a Fano hypersurface in projective space.
  • Of course, Gromov's paper, Pseudoholomorphic curves in symplectic manifolds.

Books:
  • Audin Lafontaine, Holomorphic curves in symplectic geometry.
  • McDuff-Salamon's books are good; the second one on J-holomorphic curves is good for the last lecture I gave.
  • Arnol'd, Mathematical methods of classical mechanics.
  • For the derived Fukaya category: Paul Seidel, Fukaya categories and Picard-Lefschetz theory.
 
Date &
Time:
 Saturday, December 24, 2016, 14:00-16:00
Sunday, December 25, 14:00-16:00
Monday, December 26, 14:00-16:00,  (Lecture Hall 2)
Tuesday, December 27, 14:00-16:00
Location:
 Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran


GT Seminar
Speaker:
Benjamin McKay
University College Cork, Ireland
Title: Smooth Projective Geometry
Date: Wednesday, December 7, 2016
Time: 16:00-17:30
Location: 
Lecture Hall 2,
Niavaran Building, IPM


Seminar
Speaker:
Alexander Frank
Universidad Andrés Bello, Santiago
Title: Bratteli diagrams and non-continuous eigenvalues of Cantor minimal systems of topological finite rank
Abstract: Bratteli diagrams has been used extensively these last two decades to under- stand the behavior of topological dynamical systems, in particular Cantor minimal systems (i.e. when the state space is a Cantor set). In particular, the study of eigenvalues of these systems has benefited from the use of these diagrams. As preliminaries, we introduce the notions of Bratteli diagrams, Vershik maps, eigenvalues of the Koopman operator (continuous and non-continuous) and topological rank.
Then we will see recent results on eigenvalues which generalize the classical (and seminal) results of Host on substitution dynamical systems, and other intermediate works that are in the same direction of Bressaud, Durand, Cortez and Maass. We will focus on the so-called Toeplitz systems of (topological) finite rank. These systems are not merely a particular case but they show in a clearer way which should be the conditions met for a system in order to admit non-continuous eigenvalues.
This is a joint wok with Fabien Durand and Alejandro Maass.
Date: Tuesday, November 22, 2016
Time: 14:00-15:30
Location: 
Lecture Hall 1,
Niavaran Building, IPM


Mini Course
Speaker:
Behzad Khazaie
Title: Simple Geodesics and Weil-Petersson Volumes of Moduli Spaces of Bordered Riemann Surfaces, after Maryam Mirzakhani
Abstract: In her article, M. Mirzakhani generalized the notion of moduli space of marked curves to the moduli space of bordered Riemann surfaces for studying Weil-Petersson Symplectic form on it. She gave a method for integrating geometric functions over this space and for the first time, she gave a recursive formula for calculating the volume of this moduli space of bordered Riemann surfaces. She shows that this volume function is a polynomial in the lengths of the border components. The constant term in this polynomial is the classic Weil-Petersson Volume of moduli space of curves.

In the first talk we review the basic definitions, and the main theorem. We apply the new method for the case of the moduli space of curves of genus 1 with 1 marked point using McShane identity. Then we give a vast generalization of the McShane identity that is used for the general case. In the second talk, we give the statement of the recursive formula for the volume of and prove the polynomial behavior of the volume function. Finally in the third talk, we investigate the Weil-Petersson symplectic structure and give a method to calculate the geometric functions on it. Then using the generalized McShane identity we prove the main theorem.
Date &
Time:
 Sunday, November 13, 2016 at 14:00-15:30
Tuesday, November 15, 2016 at 10:30-12:00
Tuesday, November 15, 2016 at 14:00-15:30
Location: 
Lecture Hall 2,
Niavaran Building, IPM


7th Meeting on Contemporary Mathematics
School of Mathematics, IPM
August 10-11, 2016


Speaker: 
 Gang Tian
Princeton University and Peking University
Title: 
Geometric flows and applications
Program:

14:00-15:00
16:00-17:00
Wednesday
 1st Lecture Coffee Break
2nd Lecture
Thursday 3rd Lecture Coffee Break 4th Lecture

Location: Lecture Hall 1, Niavaran Building,
School of Mathematics, IPM
Registration: The attendance is free, but requires registration.
Please fill out the registration form and
send it to gt@ipm.ir with the subject "MCM".
Poster

Homological Invariants in Low Dimensional Topology
School of Mathematics, IPM,
July 30-August 4, 2016
Speakers:
 Selman Akbulut (Michigan State University, USA)
Akram Alishahi (Columbia University, USA)
Aliakbar Daemi (Stony Brook University & SCGP, USA)
Fatemeh Douroudian (Tarbiat Modarres University, Iran)
Eaman Eftekhary (IPM, Iran)
David Gay (University of Georgia, USA)
Jennifer Hom (Georgia Tech & IAS, USA)
Ali Kamalinejad (IPM, Iran)
Robert Lipshitz (Columbia University, USA)
Ciprian Manolescu (UCLA, USA)
Organizers:
 Akram Alishahi
Aliakbar Daemi
Eaman Eftekhary
Faramarz Vafaee
Program:
 Schedule
Location: School of Mathematics, IPM,
Niavaran Square, Tehran
Registration:
 Please fill out the registration form and
send it to gt@ipm.ir with the subject "LDT".
Poster

Graduate Course
Lecturer:
 Eaman Eftekhary & Ali Kamalinejad
(School of Mathematics, IPM)
Title:
 Topology of Smooth Manifolds II
Time
& Date:		 Thursdays, 14:00-15:50 & 16:10-18:00
First lecture on Thursday, Feb. 4, 2016 (15th Bahman, 1394)

Location: Lecture Hall 2, Niavaran Building,
School of Mathematics, IPM
 
Description:


Graduate Course
Lecturer:
 Meysam Nassiri
(School of Mathematics, IPM)
Title:
 Dynamical Systems
Time
& Date:		 Thursdays, 11:00-12:20 & 12:40-14:00
First lecture on Thursday, Feb. 4, 2016 (15th Bahman, 1394)

Location: Lecture Hall 2, Niavaran Building,
School of Mathematics, IPM
 
Description:


Seminar
Speaker:
Maryam Hosseini
School of Mathematics, IPM
Title: On continuous spectrum of Cantor minimal systems
Abstract: We will discuss continuous eigenvalues of minimal systems on Cantor set. In this context, some connections to the group of values of the invariant measures on clopen sets are verified.
Date: Monday, May 9, 2016
Time: 15:00-17:00
Location: 
Lecture Hall 2,
Niavaran Building, IPM


6th Meeting on Contemporary Mathematics
School of Mathematics, IPM
February 20-22, 2016
Speaker: 
 Sophie Morel
Princeton University
Title: 
The global Langlands correspondence over function fields,
after Vincent Lafforgue
Date
&
Time: 		Saturday, February 20, 2016
  • 14:00-15:00,  Public Talk
  • 16:00-17:00,  1st Lecture

    • Sunday, February 21, 2016
  • 14:00-15:00,  2nd Lecture
  • 15:30-16:30,  3rd Lecture

    • Monday, February 22, 2016
  • 14:00-15:00,  4th Lecture
    		•

    Location: Lecture Hall 1, Niavaran Building,
    School of Mathematics, IPM
    Registration: The attendance is free, but requires registration.
    Please fill out the registration form and
    send it to gt@ipm.ir with the subject "MCM".
    		Poster

    Seminar
    Speaker:
    		Yadollah Zare
    IMPA, Brazil
    Title: Identifying an irreducible component of projective variety $M(d)$
    Abstract: In this talk, I discuss the Ilyashenko’s theorem. Let $M(d)$ be the set of all foliations of degree $d$ on $C^2$ with at least one center critical point. Also, let $S$ be the set of all foliations $F(df)$ where $f$ is a polynomial with two variables of degree $d+1$. Ilyashenko shows that $S$ is an irreducible component of $M(d)$.

    Date: Monday, February 22, 2016
    Time: 10:00-11:30
    Location: 
    		Lecture Hall 2,
    Niavaran Building, IPM


    Seminar
    Speaker:
    		Mir-Omid Haji-Mirsadeghi
    Sharif University of Technology
    Title: Point-Shift Foliation of a Point Process
    Abstract: A point-shift $F$ maps each point of a point process $\Phi$ to some point of $\Phi$. For all translation invariant point-shifts $F$, the $F$-foliation of $\Phi$ is a partition of the support of $\Phi$ which is the discrete analogue of the stable manifold of $F$ on $\Phi$. It is first shown that foliations lead to a classification of the behavior of point-shifts on point processes. Both qualitative and quantitative properties of foliations are then established. It is shown that for all point-shifts $F$, there exists a point-shift $F_\bot$, the orbits of which are the $F$-foils of $\Phi$, and which are measure-preserving. The foils are not always stationary point processes. Nevertheless, they admit relative intensities with respect to one another.
    Date: Monday, January 25, 2016
    Time: 10:00-12:00
    Location: 
    		Lecture Hall 2,
    Niavaran Building, IPM


    Seminar
    Speaker:
    		Fernando Torres
    University of Campinas, Brazil
    Title:  Curves: Hermitian/Suzuki/Ree
    Abstract: We speak about the characterization of some plane curves, Hermitian/Suzuki/Ree, over finite fields and their applications in coding theory.
    Date: Thursday, January 21, 2016
    Time: 14:30-16:00
    Location: 
    		Lecture Hall 2,
    Niavaran Building, IPM


    Seminar                                                                  (in collaboration with Frontiers in Math. Sci.)
    Speaker: 
    		 Mahdi Asgari
    Oklahoma State University
    Title: 
    		Introduction to Local Langlands Correspondence
    Abstract:
    		As part of his overall program, R. P. Langlands conjectured a certain correspondence between the set of (equivalence classes of) irreducible smooth representations of a $p$-adic reductive group and its set of $L$-parameters, i.e., certain admissible homomorphisms from the Weil group of the $p$-adic field to a certain complex group, called the $L$-group. This parameterization is to satisfy various number theoretic and representation theoretic properties involving $L$-functions and $\epsilon$-factors among other things, and lies, along with its global conjectural analogue, at the heart of the modern theory of automorphic forms and representations. When the group is $GL_n$ the correspondence is actually a bijection, now a theorem due to Michael Harris & Richard Taylor as well as Guy Henniart (around 2001) and Peter Scholze again more recently (around 2013).
    I will review some of these subjects and try to report on a recent work, joint with Kwangho Choiy, establishing the Local Langlands Conjecture for small rank general spin groups and their inner forms.
    Date: Wednesday, January 6, 2016
    Time: 15:30-17:00
    Location:
    		Lecture Hall 2,
    Niavaran Building, IPM


    Mini Course                                                              (in collaboration with Frontiers in Math. Sci.)
    Speaker:
    		 Mohammad Farajzadeh Tehrani
    Simons Center, Stony Brook University
    Title: 
    		Degeneration techniques in GW theory
    Outline:
    		 In the first talk, I will give some introduction to moduli spaces of J-holomorphic curves, absolute and relative Gromov-Witten theory, transversality issue and the Ruan-Tian approach for constructing GW invariants. The emphasis would be on relative GW theory. Next, I will talk about the GW sum formula which relates the absolute GW invariants of smooth manifolds to the GW invariants of a normal crossings degeneration. The latter can be expressed in terms of products of relative GW invariants of the smooth pieces. Finally, I will talk about a comparison theorem between absolute and relative GW invariance with respect to very positive divisors. More precisely, we compare absolute and relative Gromov-Witten invariants with the basic contact vector for very positive divisors. For such divisors, one might expect that these invariants are the same up to a natural multiple. We show that this is indeed the case outside of a narrow range of the dimension of the target and the genus of the domain. We provide explicit examples to show that these invariants are generally different inside of this range. This is joint work with A. Zinger.
    Date
    &
    Time:     		Sunday, January 3, 2016
  • 10:30-12:00,  1st Lecture
  • 13:30-15:00,  2nd Lecture

    • Monday, January 4, 2016
  • 10:30-12:00,  3rd Lecture

    		•
    Location: 
    		Lecture Hall 1,
    Niavaran Building, IPM


    Graduate Course
    Lecturers:
    		Eaman Eftekhary & Ali Kamalinejad
    (School of Mathematics, IPM)
    Title: 
    		Topology of Smooth Manifolds
    Abstract: 
    		This course is the first step in a one-year program, aimed at introducing topics in low dimensional topology and dynamical systems to starting graduate students and advanced undergraduates.

    more info
    Date: Thursdays, Fall 2015
    Time: 12:30-14:00 & 14:30-16:30
    Location: Lecture Hall 1,
    Niavaran Building, IPM
    		Poster

    GT Seminars' Archive
    April 30, 2015 - December 31, 2015
    February 19, 2015 - May 14, 2015
    November 6, 2014 - December 18, 2014
    November 7, 2013 - April 24, 2014
    July 17, 2013 - August 14, 2013
    January 7, 2013 - March 6, 2013
    October 31, 2012 - December 5, 2012
    October 5, 2011 - February 15, 2012
    May 25, 2011 - Sept 14, 2011
    Oct 13, 2010 - Dec 29, 2010
    April 28, 2010 - Sept 8, 2010
    Sept 23, 2009 - March 10, 2010

    School of Mathematics,
    IPM - Institute for Research in Fundamental Sciences
    Niavaran Building, Niavaran Square, Tehran, Iran
    Tel: +98 21 222 90 928
    		 Email: gt@ipm.ir