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Introduction to Local Langlands Correspondence
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Mahdi Asgari
(Oklahoma State University)
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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).
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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.
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Date: Wed Jan 6
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Time: 15:30-17
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Location: Lecture Hall 2, Niavaran Building, IPM

Algebraic Geometry Seminar II

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  1. Bezout’s Theorem (F. Kamankesh)
  2. Intersection Theory On Surfaces (K. Amini, R. Mahkam)
  3. Riemann-Roch and Riemann-Hurwitz Theorems (M. Jadidi, Z. Kochakzadeh)
  4. Bertini’s Theorem (A. Akhavan, A. Soofiani)
  5. Embedding of Curves in P^3 (M.Fashami)
  6. Zariski’s Main Theorem (S. Gholami, T. Torkaman)
  7. Algebraic Fundamental Group (A. Cheraghi, F. Taheri)
  8. de Rham Cohomology (P. Bagherzadeh, F. Abbasy)
  9. Hodge Structures (M. Najafpour, M. Akrami)
  10. Jacobian Of Curves (E. Shahhoseini, D. Khajehpour)
  11. Vector Bundles Over Projective Line (R. Khorram Pajouh,S. Sharifi)
  12. Vector Bundles Over Elliptic Curves (F. Amiri)
  13. Infinitesimal Criterion for Smoothness/Etaleness (?,?)
  14. Schlessinger’s Theorem (S. Tayebi)
  15. GAGA (F. Huseini, M. Rezaeian)
  16. Chow Ring (M. Fard)
  17. Leray-Hirsch Theorem For Chow Rings (B. Khazaie)

 

 

Algebraic Geometry Seminar

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Here is a pool of possible topics for the talks of the algebraic geometry seminar

  1. Bezout’s Theorem
  2. Bertini’s Theorem
  3. Embedding of Curves in P^3
  4. Zariski’s Main Theorem
  5. Vector Bundles Over Projective Line
  6. Vector Bundles Over Elliptic Curves
  7. Infinitesimal Criterion for Smoothness/Etaleness
  8. Schlessinger’s Theorem
  9. de Rham Cohomology
  10. Riemann-Roch and Riemann-Hurwitz Theorems
  11. Algebraic Fundamental Group
  12. GAGA
  13. Chow Ring
  14. Intersection Theory On Surfaces
  15. Jacobian Of Curves
  16. Leray-Hirsch Theorem For Chow Rings

Each of the above topics will be given to a group consisting of two participants.  To select a topic please make an appointment with Dr. M. Asgharzadeh. The time schedule will be announced subsequently.

 

 

Special Year On Langlands Program

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This Program will be held during the academic year 2015-2016 through the collaboration of the following organizations, Institute for Research in Fundamental Sciences (IPM), Sharif University Of Technology and Tarbiat Modares University. The upcoming program has been proposed and established under the supervision of Prof. F. Shahidi, with the following twofold aims. First, to arouse the interest of participants (including graduate and even undergraduate students) on one of the deepest and most exciting web of mathematical theories. Second, to provide necessary materials to introduce the participants to the geometric and arithmetic  aspects of the Langlands program, that may further help them to obtain some primary insights about the prescribed analogy between these different aspects. In addition we hope that the program provides essential background materials for the one month conference that will be held during summer 2016 in the framework of Frontiers in Math.

Accordingly we desire that the following topics

1 – Algebraic Number Theory
2 -Theory of schemes
3 – Introduction to algebraic curves and Riemann surfaces
4 – Class field theory
5 – Introduction to algebraic stacks
6 – Introduction to Shimura varieties and their analogs over function fields
7 – Introduction to the theory of motives
8 – Algebraic Groups and Representation Theory
9 – Automorphic Forms
10- Iwasawa Theory

will be covered by series of courses and short courses during the upcoming winter and spring semesters. Note that the following courses has been already launched for the winter semester 2015-2016

1-Algebraic Number Theory (Dr. M. Shahshahani, Place: Sharif University, Sundays and Tuesdays 15:00-17:00)

2-Class Field Theory: with Group Cohomological Approach (Dr. A. Jafari, Place: Sharif University,  Saturdays and Mondays 15:00-17:00);

3-Scheme Theory (Dr. M. Asgharzadeh, Place: IPM, Thursdays 8:00-12:00)

We  also strongly recommend the participants to attend the following course

Topology Of Smooth Manifolds (Dr. E. Eftekhary, Dr. A. Kamalinejad, Thursdays 12:00-16:00 )

Additional information about courses and short courses will subsequently be announced in this web page.

For the registration process the applicants are required to send the documents

1- Curriculum Vitae(CV)

2-Motivation Letter (at most 15 lines)

to the following e-mail address

shabibi@ipm.ir

Please indicate  if  you wish to receive financial assistance.
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Deadline for registration 19 Sept 2015
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Organizing Committee: Dr. A. Rajaei, Dr. A. Kamalinejad, Dr. E. Arasteh Rad and Dr. S. Habibi