February 2

• Speaker: Ajmain Yamin

• Title: First Meeting

• Meeting agenda: We will figure out how we intend to run this seminar.  We may finish up some exercises from Part I of the book or move on to Part II Brauer groups: Chapter 5 on Skewfields, algebras, and modules.

February 9

• Speaker: Connor Stewart

• Title: Modules and endomorphisms

• Meeting agenda: Connor will continue presenting Chapter 5: Skewfields, algebras, and modules.  Last time Connor presented most of Section 1: Skewfields and algebras.  This time, Connor will begin presenting Section 2: Modules and endomorphisms and move on to Section 3: Semisimplicity if there is time.

February 16

• Speaker: Ajmain Yamin

• Title: The radical and matrix algebras

• Meeting agenda: Connor will finish presenting Section 3: Semisimplicity and Ajmain will pick up by presenting Section 4: The radical and Section 5: Matrix algebras.

February 23

• Speaker: Ajmain Yamin

• Title: The radical and matrix algebras

• Meeting agenda: Ajmain will continue presenting Section 4: The radical and Section 5: Matrix algebras.

March 2

• Speaker: Ajmain Yamin

• Title: Matrix algebras

• Meeting agenda:  Ajmain will finish presenting Section 5: Matrix algebras.

March 9

• Speaker: N/A

• Title: N/A

• Meeting agenda:  There will be no meeting this week as there will be the Lightning Talks on Wednesday March 9th 4-6pm in the Math Lounge.

March 16

• Speaker: Ajmain Yamin

• Title: Review of Chapter 5 - Skewfields, algebras, and modules

• Meeting agenda:  Ajmain will give a brief review of Chapter 5 - Skewfields, algebras, and modules which will be recorded.  After this, we will begin discussing exercises from Chapter 5.

March 23 & 30

• Speaker: N/A

• Title: Chapter 5 exercises

• Meeting agenda:  We will spend two meetings discussing exercises from Chapter 5.

April 6 & 13

• Speaker: Ajith Nair

• Title:  Central simple algebras

• Meeting agenda:  Ajith will begin presenting Chapter 6 - Central simple algebras.

April 20 & 27

• Speaker: Ajith Nair

• Title: Tensor products and the group law

• Meeting agenda:  There was no meeting on April 20, as it was Spring break.  On April 27, Ajith will finish his presentation on Section 2: Tensor products and perhaps cover Section 3: The group law, if there is time.  This will be the last meeting of the Spring 2022 semester.

Meeting Details

• The first meeting will be on Wednesday June 22 9 AM- 11 AM Eastern Time.  

• The meetings will be held virtually through zoom

• Send an email to ayamin(at)gradcenter(dot)cuny(dot)edu for the permanent zoom link.

June 22 @ 9 AM - 11 AM Eastern Time

• Speaker: Connor Stewart

• Title: The fundamental theorems

• Meeting agenda: Connor will begin presenting the rest of Chapter 6: Central Simple Algebras starting with Section 4: The fundamental theorems.

June 29 @ 9 AM - 11 AM Eastern Time

• Speaker: Connor Stewart

• Title: Splitting fields and Separability

• Meeting agenda:  Connor will finish presenting Chapter 6: Central Simple Algebras by presenting Section 5: Splitting fields and Section 6: Separability.  Connor will also start presenting Chapter 7: Combinatorial constructions Section 1: Introduction.

July 6 @ 9 AM - 11 AM Eastern Time

• Speaker: Ajmain Yamin

• Title: Group extensions and First applications: cyclic groups

• Meeting agenda:  Ajmain presented Chapter 7: Combinatorial Constructions Section 2: Group extensions and Section 3: First applications: cyclic groups.

July 21 @ 9:30 AM - 11:15 AM Eastern Time

• Speaker: Ajith Nair

• Title: Crossed product algebras

• Meeting agenda: Ajith presented Chapter 7: Combinatorial Constructions Section 4: Crossed product algebras.

July 27 @ 9 AM - 10 AM Eastern Time

• Speaker: Ajith Nair

• Title: Compatibilities

• Meeting agenda: Ajith started presenting Section 5: Compatibilities.

Meeting Details

• There will be weekly meetings on Wednesdays at 12:00 PM - 1:45 PM.

• The meetings will be at the Graduate Center, Math Thesis Room (4214.03).

• Depending on interest, we may stream the talks through zoom. Email ayamin(at)gradcenter(dot)cuny(dot)edu if you are interested in participating in the seminar but cannot attend in-person.

September 14

• Speaker: Ajmain Yamin

• Title: First meeting - Galois Cohomology 

• Meeting agenda: Ajmain will initiate new participants to the seminar.  I will go over goals and objectives for CUNY CFT Student Learning Seminar.  We will draft a schedule of talks for the Fall 2022 semester.  Please attend this meeting if you are curious about attending/participating in the seminar.  In the Fall semester, we will be starting Part III of Pierre Guillot's book, which is on Galois Cohomology.  The main focus of this seminar will be to present the majority of the four chapters which constitute Part III:
  Chapter 9: Ext and Tor
  Chapter 10: Group cohomology
  Chapter 11: Hilbert 90
  Chapter 12: Finer structure
  Please note: you do not need to have participated in previous semesters of the CUNY CFT Student Learning Seminar to follow along in this semester!  Part III of Guillot's book is almost entirely independent from the previous sections of the book.  

September 21

• Speaker: Susan Rutter

• Title: Complexes and The Ext groups

• Meeting agenda:  Last week Ajmain covered Section 1: Preliminaries and Section 2: Resolutions of Chapter 9: Ext and Tor.  This week, Susan will begin presenting Section 3: Complexes and Section 4: The Ext groups.

September 28

• Speaker: Valera Sergeev

• Title: Long exact sequences and The Tor Groups

• Meeting agenda: Valera will be presenting the remaining sections of Chapter 9: Ext and Tor, namely Section 5: Long exact sequences and Section 6: The Tor groups.

October 12

• Speaker: None

• Title: Exercises from Chapter 9: Ext and Tor

• Meeting agenda: This meeting will be a problem solving session for the exercises in Chapter 9: Ext and Tor.

October 26

• Speaker: Ajith Nair

• Title: Definition of group (co)homology and The standard resolution

• Meeting agenda:  Ajith began presenting Chapter 10: Group cohomology, Section 1: Definition of group (co)homology and Section 2: The standard resolution.

November 2

• Speaker: Ajith Nair and Connor Stewart

• Title: The standard resolution, Low degrees, and Profinite groups and Galois cohomology

• Meeting agenda: Ajith will finish presenting Chapter 10: Group cohomology, Section 2: The standard resolution and Connor will begin presenting Section 3: Low degrees and Section 4: Profinite groups and Galois cohomology.

November 9

• Speaker: Connor Stewart

• Title: Low degrees, Profinite groups and Galois cohomology

• Meeting agenda:  Connor will finish up the presentation of Chapter 10: Group cohomology, Section 3: Low degrees and Section 4: Profinite groups and Galois cohomology.

November 16

• Speaker: Ajmain Yamin

• Title: Kummer theory, Hilbert 90 in Galois cohomology and More Kummer theory

• Meeting agenda:  Ajmain will give a brief review of Chapter 1: Kummer Theory and move on to present the first two sections of Chapter 11: Hilbert 90, Section 1: Hilbert 90 in Galois cohomology and Section 2: More Kummer theory.  If there is time, Ajmain will prove Proposition 7.18 of Section 3: First applications: cyclic groups of Chapter 7: Combinatorial Constructions, which will be relevant for Valera's presentation next week.

November 23

• Speaker: Valera Sergeev

• Title: The Hilbert symbol

• Meeting agenda: Valera will complete the presentation of Chapter 11: Hilbert 90 by presenting Section 3: The Hilbert symbol.  If there is time, we will do exercises.

Meeting Details

• There will be weekly meetings on Mondays at 12:00 PM - 1:45 PM.

• The meetings will be at the Graduate Center, Math Thesis Room (4214.03).

• Depending on interest, we may stream the talks through zoom. Email ayamin(at)gradcenter(dot)cuny(dot)edu if you are interested in participating in the seminar but cannot attend in-person.

January 30

• Speaker: Ajmain Yamin

• Title: Review of Galois Cohomology

• Meeting agenda:  Ajmain will give a review of the first three chapters of Part III: Galois Cohomology, namely, Chapter 9: Ext and Tor, Chapter 10: Group Cohomology and Chapter 11: Hilbert 90. 

February 6

• Speaker: Valera Sergeev

• Title: Shapiro's isomorphism and A few explicit formulae

• Meeting agenda: Valera will begin presenting Chapter 12: Finer Structure by presenting Section 1: Shapiro's isomorphism and Section 2: A few explicit formulae.

February 13 (Zoom meeting)

• Speaker: Connor Stewart

• Title: The corestriction

• Meeting agenda: Connor presented most of Chapter 12, Section 3: The corestriction.

February 27

• Speaker: Connor Stewart

• Title: The conjugation action

• Meeting agenda:  Connor will present the rest of Section 3 and present Section 4: The conjugation action.

March 20

• Speaker: Ajmain Yamin

• Title: The five-term exact sequence

• Meeting agenda:  Ajmain will begin presenting Section 5: The five-term exact sequence.

March 27

• Speaker: Ajith Nair

• Title: Cup-products

• Meeting agenda: Ajith will begin presenting Section 6: Cup-products.

April 3

• Speaker: Ajith Nair

• Title: Cup-products

• Meeting agenda: Ajith will continue presenting Section 6: Cup-products.

April 17

• Speaker: Ajith Nair and Valera Sergeev

• Title: Cup-products, Milnor and Bloch-Kato

• Meeting agenda: Ajith will finish presenting Section 6: Cup-products and Valera will present Section 7: Milnor and Bloch-Kato.  If there is time remaining, we will do some exercises from Chapter 12: Finer Structure.

April 24

• Speaker: N/A

• Title: Exercises from Chapter 12: Finer Structure

• Meeting agenda:  This will probably be the last meeting of the semester.  We will do exercises from Chapter 12: Finer Structure.

Meeting Details

• There will meetings every other Friday from 10:00 AM - 11:00 AM.

• The meetings will be at the Graduate Center, Math Thesis Room (4214.03).

• Email ayamin(at)gradcenter(dot)cuny(dot)edu if you wish to be put on the mailing list.

September 8

• Speaker: Ajmain Yamin

• Title: Statements of Local Class Field Theory

• Meeting agenda:  Ajmain started presenting Chapter 13: Local Class Field Theory of Part IV: Class Field Theory of Guillot's book.

September 22

• Speaker: Connor Stewart

• Title: Cohomological triviality and equivalence

• Meeting agenda:  Connor will present Section 2: Cohomological triviality and equivalence of Chapter 13.  The goal is to prove Tate's theorem which will be used to deduce the reciprocity theorem of local class field theory.

October 6

• Speaker: Connor Stewart and Ajmain Yamin

• Title: Cohomological triviality and equivalence

• Meeting agenda:   Connor finished presenting Section 2: Cohomological triviality and equivalence of Chapter 13.  Then Ajmain presented the proof of Proposition 8.4, showing that the norm subgroups corresponding to the degree n unramified extensions of a local number field are precisely the kernels of the valuation map mod n.

October 20

• Speaker: Ajmain Yamin

• Title: The Brauer group of a local number field

• Meeting agenda:  Ajmain will begin the meeting by presenting Chapter 8: The Brauer group of a local number field. Ajmain will present Section 8.2: The Hasse invariant of a skewfield and Section 8.3: Naturality.  

November 3

• Speaker: Ajmain Yamin

• Title: The Brauer group of a local number field

• Meeting agenda:  Ajmain continued presenting Chapter 8: The Brauer group of a local number field.

November 17

• Speaker: Valera Sergeev

• Title: Norms subgroups

• Meeting agenda:  Valera will present Section 14.2: The reciprocity isomorphisms and Section 14.3: Norm subgroups.

Meeting Details

• There will meetings every Wednesday from 12:00 PM - 1:00 PM.

• The meetings will be at the Graduate Center, Math Thesis Room (4214.03).

• Email ayamin(at)gradcenter(dot)cuny(dot)edu if you wish to be put on the mailing list.

February 21

• Speaker: Ajmain Yamin

• Title: Review and the Existence theorem 

• Meeting agenda:  Ajmain will review what has been covered of Chapter 13: Local Class Field Theory so far.  Namely, the first four sections.  Then, Ajmain presented Section 13.6: The Existence theorem.

March 13

• Speaker: Ajith Nair

• Title: Tate duality

• Meeting agenda:  Ajith will present Section 13.5: Tate duality.

March 20

• Speaker: Ajmain Yamin

• Title: Tate duality

• Meeting agenda:  Ajmain will finish presenting Section 13.5: Tate duality.

March 28

• Speaker: Valera Sergeev

• Title: The local Kronecker-Weber theorem

• Meeting agenda: Valera will present Section 13.6: The local Kronecker-Weber theorem.  

April 3

• Speaker: Valera Sergeev

• Title: The local Kronecker-Weber theorem

• Meeting agenda: Valera will finish presenting Section 13.6 and some relevant lemmas from Part I of the book.

April 17

• Speaker: Connor Stewart

• Title: A concise reformulation

• Meeting agenda: Connor will present Section 13.7: A concise reformulation.  If there is time remaining, Connor will start presenting Chapter 14: Global Class Field Theory.

May 1

• Speaker: Connor Stewart

• Title: Number fields, their completions, the discriminant & the (global) Kronecker-Weber theorem

• Meeting agenda: Connor will present Section 14.1: Number fields and their completions, Section 14.2: The discriminant, and Section 14.3: The (global) Kronecker-Weber Theorem.

May 8

• Speaker: Joseph DiCapua

• Title: Formal Group Laws and Explicit Local Class Field Theory

• Meeting agenda: Joe will give an introduction to Lubin-Tate formal group laws and the application to explicit local class field theory.