Course notes
These are scanned course notes from various courses I have taken as well some I have taught. The instructor is listed along with the course notes. Any errors in the notes are most likely due to my misunderstanding at the time and not due to the instructor. Please use these at your own risk, I have not checked them recently to make sure they are free of errors.
- Algebraic Number Theory (Chris Skinner, Fall 2000, 205 pages)
- Class Field Theory (Brian Conrad, Spring 2001, 377 pages)
- Differentiable manifolds (Krishnan Shankar, Fall 2001, 151 pages)
- Analytic Number Theory (Kannan Soundararajan, Fall 2001, 159 pages)
- Algebraic Geometry 1 (Karen Smith, Fall 2001, 99 pages)
- Modular Forms (Brian Conrad, Fall 2001, 123 pages)
- Iwasawa Theory (Chris Skinner, Spring 2002, 154 pages)
- Algebraic Geometry 2 (Karen Smith, Spring 2002, 172 pages)
- Algebraic Curves (Rob Lazarsfeld, Spring 2002, 132 pages)
- Modular Forms (Kannan Soundararajan, Fall 2002, 194 pages)
- Elliptic Curves (Brian Conrad, Fall 2003, 184 pages)
- Zeros of L-functions and random matrix theory (Kannan Soundararajan, Spring 2004, 238 pages)
- Iwasawa Theory (Univ. of Michigan Graduate Students, Summer 2004 reading course, 85 pages)
- Introduction to Iwasawa Theory (Jim Brown, Fall 2006, 102 pages)
- Introduction to number theory (Jim Brown, Spring 2007, 256 pages)
- Local class field theory (Jim Brown, Winter 2008, 97 pages)
- Global class field theory (Jim Brown, Spring 2008, 186 pages)
- Introduction to Topology (Jim Brown, Fall 2009, 287 pages)
- Abstract Algebra (Jim Brown, Fall 2010 - Spring 2011, 520 pages)
- Graduate Linear Algebra (Jim Brown, Summer 2014, 209 pages)
Notes from conference talks
These are notes I have taken at various conferences. Any errors are most likely due to my lack of understanding or not being able to keep up.
- Automorphic Galois representations, L-functions, and arithmetic at Columbia University, June 17-22, 2006
- The critical values of L-functions by Don Blasius
- Lectures on integral representations of L-functions by Jim Cogdell
- Nonvanishing of L-values by Haruzo Hida
- Tamagawa number conjecture and Iwasawa main conjectures by Guido Kings
- Eisenstein series I by Erez Lapid
- Eisenstein series II by Erez Lapid
- On the Eisenstein ideal for U(2,1) by Fabio Mainardi
- p-adic L-functions by Chris Skinner
- Hida theory for U(n,n) by Eric Urban
- Special values of L-functions modulo p by Nike Vatsal
- Summer school in Iwasawa theory at McMaster University, August 9-13, 2007
- Introduction to Iwasawa theory by Ralph Greenberg
- Iwasawa theory of elliptic curves by Rob Pollack
- Eisenstein ideals and main conjectures in Iwasawa theory by Eric Urban
- Selmer groups, L-functions, and Galois deformations at UCLA, March 24-29, 2008
- Families of Galois representations and families of automorphic forms -- an introduction by Frank Calegari (March 24)
- Hida families for GL(2) over totally real fields by Mladen Dimitrov (March 24)
- Construction of p-adic L-functions for unitary groups I by Michael Harris (March 24)
- Growth of Selmer rank in nonabelian extensions of number fields by Karl Rubin (March 25)
- Construction of p-adic L-functions for unitary groups II by Chris Skinner (March 25)
- Heegner points, Iwasawa theory, and the Gross-Zagier theorem by Ben Howard (March 27)
- Periods and heights of Heegner points by Shou-wu Zhang (March 27)
- How many automorphic forms are there over imaginary quadratic fields? by Frank Calegari (March 28)
- Tate-Shafarevich groups over anticyclotomic Z_{p} extensions at supersingular primes by Mirela Ciperani (March 28)
- Ikeda's conjecture on the period of the Ikeda lifting by Hisa-aki Kawamura (March 29)
- Modular forms and arithmetic (Ken Ribet's 60th birthday Conference) at MSRI, June 28 - July 2, 2008
- Construction of abelian extensions following Ribet by Barry Mazur (June 28)
- Ken Ribet and Fermat's last theorem by Kevin Buzzard (June 28)
- Lang-Trotter revisited and lower bounds for Frobenius traces by Nick Katz (June 28)
- On l-adic families of admissible representations of GL_{2}(Q_{p}) by David Helm (June 29)
- Kolyvagin's approach to the Birch and Swinnerton-Dyer conjecture by William Stein (June 29)
- Level lowering for p-adic modular forms by Matthew Emerton (June 30)
- Non-trivial extensions of p-adic Galois representations that are trivial at p by Joel Bellaiche (July 1)
- Modular symbols for global fields by Loic Merel (July 1)
- PANTS IX at Clemson University, February 7-8, 2009
- Introduction to p-adic L-functions by Jim Brown (February 9)
- L-functions, p-adic L-functions, and rational points by Kartik Prasanna (February 9)
- PCMI/IAS: Arithmetic of L-functions at Park City Mathematics Institute, Park City, Utah, June 29-July 17, 2009
- Restricted Selmer groups and special values of p-adic L-functions by Adebisi Agboola
- The ETNC for Dirichlet L-functions at s=0 by David Burns
- Tate-Shafarevich groups of elliptic curves over anticyclotomic Z_{p} extensions by Mirela Ciperiani
- An Euler system for automorphic symplectic motives by Cristophe Cornut
- Modular forms and the Gross-Stark conjecture by Samit Dasgupta
- Iwasawa theory and projective modules by Ralph Greenberg
- The arithmetic of elliptic curves - an update by Benedict Gross
- Lectures on the conjecture of Birch and Swinnerton-Dyer by Benedict Gross
- Self-dual and conjugate-dual Galois representations by Benedict Gross
- Serre curves in one parameter families by Nathan Jones
- Iwasawa theory for supersingular primes by Byoung Du Kim
- The equivariant Tamagawa number conjecture and the Birch-Swinnerton-Dyer conjecture for elliptic curves by Guido Kings
- Special values of L-functions at negative integers by Manfred Kolster
- Growth of L-values in towers by Robert Pollack
- Integral and p-adic refinements of the abelian Stark conjecture(presented at board) by Cristian Popescu
- Integral and p-adic refinements of the abelian Stark conjecture (typed version) by Cristian Popescu
- Non-optimal levels of reducible Galois representations by Ken Ribet
- Root Numbers by David Rohrlich
- Euler systems and Kolyvagin systems by Karl Rubin
- Refined class number formulas and Kolyvagin systems by Karl Rubin
- Selmer groups for reducible representations by Romyar Sharifi
- Introduction to elliptic curves by Alice Silverberg
- Stark's basic conjecture by John Tate
- Stark's basic conjecture II by John Tate
- Elliptic curves over function fields I by Douglas Ulmer
- Elliptic curves over function fields II by Douglas Ulmer
- Elliptic curves over function fields III by Douglas Ulmer
- Complex Multiplication I by Nike Vatsal
- Complex Multiplication II by Nike Vatsal
- Complex Multiplication III by Nike Vatsal
- PANTS X at Armstrong Atlantic State University, September 19-20, 2009
- Some background on elliptic curves and Galois cohomology by Jim Brown (September 19)
- The Birch and Swinnerton-Dyer conjecture by Amod Agashe (September 19)
- PANTS XI at University of South Carolina, December 4-5, 2009
- Mean values of multiplicative functions and applications by Kannan Soundararajan (December 5)
- PANTS XII at Clemson University, February 20-21, 2010
- On the degree 5 L-function for GSp(4) by Dan File (February 20)
- Amicable pairs for elliptic curves by Joseph Silverman (February 20)
- L-functions, modularity, and functoriality by James Cogdell (February 21)
- Conference in honor of Fontaine, IHP Paris, France, March 22-26, 2010
- On the Iwasawa theory of modular forms by Matt Emerton (March 25)
- Extensions of Iwasawa modules I by Chandrashekhar Khare (March 22)
- Potential automorphy for compatible systems of l-adic representations by Richard Taylor (March 22)
- Solvable points on curves by Andrew Wiles (March 18)
- Modular/Geometric Iwasawa Theory and p-adic L-functions, UCLA, June 14-20, 2010
- Hida families and Gross-Stark units over totally real fields
- p-adic Rankin-Selberg convolutions
- Lecture 1 by Fabian Januszewski
- Noncommutative main conjecture of Iwasawa theory for totally real number fields
- Lecture 1 by Mahesh Kakde
- p-adic L-functions and the Griffiths group
- Galois cohomology, Iwasawa theory, and p-adic L-functions
- Lecture 1 by Romyar Sharifi
- Pullback formulas, differential operators and construction of p-adic families of holomorphic cusp forms for unitary groups
- Algebraicity of L-functions for GL(2)
- PANTS XV at Clemson University, February 19-20, 2011
- p-adic variants of the Birch and Swinnerton-Dyer conjecture by Adebisi Agboola (February 19)
- 2011 Arizona Winter School at University of Arizona, March 12-16, 2011
- Stark-Heegner points by Henri Darmon and Victor Rotger
- Notes provided
- Lecture 4 by Darmon
- The rank one abelian Stark conjecture by Samit Dasgupta and Matthew Greenberg
- Notes provided
- Lecture 1 by Dasgupta
- Lectures 2-3 by Greenberg
- Lecture 4 by Dasgupta
- Overconvergent modular symbols by Robert Pollack and Glenn Stevens
- Notes provided
- Lectures 1-3 by Pollack
- Lecture 4 by Stevens
- Periods and special values of L-functions by Kartik Prasanna
- Notes provided
- Lectures 1-4 by Prasanna
- Stark-Heegner points by Henri Darmon and Victor Rotger
- Workshop on Galois Representations and Automorphic Forms at IAS, March 21-25, 2011
- Local-global compatibility and monodromy by Ana Caraiani
- Minimal modularity lifting theorems for imaginary quadratic fields by Frank Calegari
- The proof of the Burger-Sarnak conjecture by Laurent Clozel
- An overconvergent Eichler-Shimura map by Adrian Iovita
- Supercuspidal L-packets by Tasho Kaletha
- Construction of eigenvarieties and coherent cohomology by Vicent Pilloni
- A semistable model for the tower of modular curves by Jared Weinstein
- FRG/RTG Workshop on L-functions, Galois Representations and Iwasawa Theory at University of Michigan, May 17-22, 2011
- Minimal modularity lifting theorems over imaginary quadratic fields by David Geraghty
- On growth of Hecke fields in a p-adic family and its applications by Haruzo Hida
- Arithmetic intersection theory and unitary Shimura varieties by Ben Howard
- An overview of the theory of Eisenstein series by Freydoon Shahidi
- My notes (first two talks only)
- Introduction to Shimura varieties by Sug Woo Shin
- Ranks of Selmer groups of elliptic curves part II by Chris Skinner
- Ranks of Selmer groups of elliptic curves part I by Eric Urban
- Nonabelian local class field theory and the geometry of Lubin-Tate spaces by Jared Weinstein
- The Birch and Swinnerton-Dyer Conjecture Summer School at Porto Conte Ricerche, Alghero, Italy, June 26 - July 3, 2011
- Birch-Swinnerton-Dyer and partiy by Vladimir Dokchitser
- L-functions and root numbers by Tim Dokchitser
- Modular symbols and BSD over abelian fields by Christian Wuthrich
- PANTS XVII at Clemson University, December 3-4, 2011
- Dodecic 3-adic fields by Chad Awtrey
- Ternary quadratic forms and half-integral weight modular forms by Alia Hamieh
- Conjectural extensions of the Gross-Zagier Theorem by Ben Howard (notes by Jim Brown)
- Constructions of automorphic forms by Dihua Jiang
- Mock modular forms and their shadows by Zach Kent
- Modularity of Galois representations over imaginary quadratic fields by Kris Klosin
- Ingrality properties of the CM-values of certain weak Maass forms by Larry Rolen
- Families of automorphic L-functions by Sug Woo Shin
- Cohomology of Bianchi groups by Seyfi Turkelli
- Modular forms and elliptic curves over the cubic field of discriminant -23 by Dan Yasaki
- On Saito-Kurokawa lifts by Dania Zantout
- Automorphic forms and related geometry at Yale University, New Haven, CT, April 23-27, 2012
- The endoscopic classification of representations by Jim Arthur
- Converse theorems by Jim Cogdell
- Stability and the local Langlands correspondence by Freydoon Shahidi
- Automorphic descent from GL(n) to classical groups by David Soudry
- Automorphic forms and Galois representations by Richard Taylor
- Spherical varieties and the relative Langlands program by Akshay Venkatesh
- Building Bridges: 1st EU-US conference on automorphic forms and related topics at RWTH Aachen University, Aachen, Germany, August 6-10, 2012
- Borcherds products and singular theta lifts for orthogonal and unitary groups by Jens Funke
- Siegel zeroes by Jeff Hoffstein
- On computations of half-integral weight modular forms by Nils Skoruppa
- PANTS XVIII at Wake Forest University, September 15-16, 2012
- Higher theta functions by Sol Friedberg
- Selmer ranks of quadratic twists of elliptic curves by Zev Klagsbrun
- PANTS XIX at the University of South Carolina, December 1-2, 2012
- Workshop on Bianchi and Siegel modular forms, University of Sheffield, Sheffield, United Kingdom, July 14-16, 2014
- Congruence primes via higher L-functions by Siegfried Bocherer
- Langlands functoriality and Harder's conjecture by Neil Dummigan
- Congruences and R=T theorems by Kris Klosin
- Non-vanishing of fundamental Fourier coefficients of Siegel modular forms by Jolanta Marzec
- Local and global Maass relations by Ameya Pitale
- Siegel modular forms of degree 2: Fourier coefficients, L-functions, and functoriality by Abhishek Saha
- Cohomology of Bianchi groups and arithmetic by Haluk Sengun
- Big images of Galois representations and congruence ideals by Jacques Tilouine
- Diagonalising spaces of Siegel Eisenstein series by Lynne Walling
- Automorphic forms, Shimura varieties, Galois representations and L-functions (Michael Harris' 60th Birthday Conference), MSRI, December 1-5, 2014
- Finite dimensional Banach spaces by Pierre Colmez
- Moduli stacks of local Galois representations by Matt Emerton
- Cycles on Shimura varieties and applications to Faltings heights by Ben Howard
- p-adic L-functions, Iwasawa theory, and elliptic curves by Chris Skinner
- Parabolically induced mod p representations of reductive p-adic groups by Marie-France Vigneras
- Euler systems by Sarah Zerbes
- SERMON XXVII at Winthrop University, March 28-29, 2015
- Unlikely intersections in complex dynamics by Holly Krieger
- Special values of L-functions by Ameya Pitale
- The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders by Ila Varma
- PANTS XXV at Clemson University, December 5-6, 2015
- $p$-adic $L$-functions and the geometry of Hida families by Joe Kramer- Miller
- $L$-functions of Siegel modular forms by Aaron Pollack
- Galois Representations and Automorphic Forms, Polish Academy of Sciences, Bedlewo, Poland, August 14-20, 2016
- Deformations of Saito-Kurokawa type II by Tobias Berger
- Geometric Serre weights for Hilbert modular forms by Fred Diamond
- Weil-etale cohomology and Zeta functions of arithmetic schemes by Matthias Flach
- Cuspidal vs. Eisenstein cohomology by Gunter Harder
- General Serre weight conjectures by Florian Herzig
- Hida families and $p$-adic triple product $L$-functions by Ming Lun Hsieh
- Deformations of Saito-Kurokawa type I by Krzysztof Klosin
- Beyond the main conjecture in Iwasawa theory by Cristian Popescu
- Picard modular surfaces, residual Albanese quotients and rational points by Dinakar Ramakrishnan
- Moduli stacks of potentially Barsotti-Tate Galois representations by David Savitt
- Arithmetic of Picard modular surfaces modulo an inert prime by Ehud de Shalit
- Main conjectures and special values of $L$-functions by Christopher Skinner
- Galois representations and adelic point groups by Peter Stevenhagen
- Congruence ideals and Selmer groups for higher symmetric powers by Jacques Tilouine
- Euler systems and deformations of Galois representations by Eric Urban
- On Galois representations of mod $p$ Hilbert eigenforms of weight one by Gabor Wiese
Notes from seminar talks
These are notes I have taken at various seminars. Any errors are most likely due to my lack of understanding or not being able to keep up.
- The Birch and Swinnerton-Dyer conjecture through Siegel modular forms and Galois representations by Chris Skinner (U of Mich. 9-16-2002)
- Main conjectures for modular forms by Chris Skinner (U. of Mich. 3-29-2004)
- Anticyclotomic μ-invariants of elliptic curves by Tom Weston (Ohio State 1-22-2007)
- The Skinner-Wiles trick for GSp(4) by Claus Sorenson (Caltech 2-14-2008)
- Aspects of non-abelian Lubin-Tate theory by Teruyoshi Yoshida (Caltech 3-8-2008)
- p-adic Beilinson and Bloch-Kato conjectures by Tejawi Navilarekallu (Caltech 5-1-2008)
- Galois representations arising from some compact Shimura varieties by Sug Woo Shin (Caltech 5-8-2008)
- Solving Diophantine equations with analysis by Tonghai Yang (Clemson 2-5-2009)
- Introduction to the number theory of function fields and Drinfeld modules by Matt Papanikolas (Clemson 4-16-2009)
- Drinfeld modular forms and Drinfeld modular curves by Matt Papanikolas (Clemson 4-16-2009)
- Arithmetic of function field gamma and zeta functions by Matt Papanikolas (Clemson 4-17-2009)
- Introduction to the Hodge conjecture by Jim Brown (Clemson REU 6-18-2009)
- Arithmetic Avatars of Analytic Objects: A case study using the Yoshida lift by Johnson Jia (Clemson 12-03-09)
- A primitive p-integral Yoshida lift by Johnson Jia (Clemson 12-04-09)
- Quantum Unique Ergodicity and Number Theory by Kannan Soundararajan (Univ. of South Carolina Colloquium 12-04-09)
- The degree five L-function for GSp(4) and Bessel coefficients by Dan File (Clemson University 2-19-10)
- On sums of three squares by Jim Cogdell (Clemson University 2-19-10)
- Moments of zeta and L-functions by Kannan Soundararajan (Athens-Atlanta Number Theory Seminar 2-1-11)
- Modularity of residually reducible Galois representations by Kris Klosin (Clemson University 12-1-11)
- Polynomial equations modulo p by Matt Boylan (Clemson REU 6-14-12)
- Introduction to modular symbols by Rodney Keaton (Clemson University 9-5-12)
- Conic theta functions by Winfried Kohnen (Clemson University 11-29-12)
- p-adic families of Eisenstein series for unitary groups by Ellen Eischen (Clemson University 4-24-13)
- An explicit semi-factorial model of the Neron model by Jesse Kass (Clemson University 3-26-14)
- Level stripping for genus 2 Siegel modular forms by Rodney Keaton (Clemson University 4-19-14)
- Geometry of Numbers Methods over Number Fields by Arul Shankar (Athens-Atlanta Number Theory Day Fall 2014)
- Kolyvagin's Conjecture on Heegner Points by Wei Zhang (Athens-Atlanta Number Theory Day Fall 2014)
- The Chowla-Selberg formula for quartic abelian CM fields by Robert Cass (Clemson University 3-24-14)
- The mean number of 3-torsion elements in ray class groups of quadratic fields by Ila Varma (Clemson University 3-26-15)
- Motivic cohomology actions and the geometry of eigenvarieties by David Hansen (Columbia University 9-11-15)
- The Iwasawa main conjecture for elliptic curves at supersingular primes by Florian Sprung (Joint NYC Seminar 10-1-15)
- The BSD conjecture and generalized Kato classes by Henri Darmon (Joint NYC Seminar 10-8-15)
- On vanishing of torsion in the cohomology of Shimura varieties by Ana Caraiani (Joint NYC Seminar 10-23-15)
- Algebraic flows on abelian varieties and Shimura varieties by Emmanuel Ullmo (Joint NYC Seminar 11-5-15)
- Average numbers of integral points in dynamical orbits by Wade Hindes (CUNY Collaborative Number Theory Seminar 11-13-15)
- Local Langlands for simple supercuspidal representations of SO($2 \ell + 1, F)$ by Moshe Adrian (CUNY Collaborative Number Theory Seminar 11-20-15)
- Congruence ideals and Selmer groups for symmetric powers by Jacques Tilouine (Columbia Automorphic Forms Seminar 2-5-16)
- Congruence primes for automorphic forms on unitary groups by Jim Brown (CUNY Collaborative Number Theory Seminar 2-5-16)
- Algebraic knot invariants, arithmetic knot theory, and asymptotics by Alison Miller (Joint NYC Seminar 2-11-16)
- A quantum algorithm for computing the unit group of a number field by Kirsten Eisentraeger (Joint NYC 2-18-16)
- Rationality of canonical heights by Laura DeMarco (Joint NYC 2-25-16)
- On the Drinfeld moduli problem of $p$-divisible groups by Michael Rapoport (Columbia 2-26-16)
- The asymptotic behavior of periods of automorphic forms by Simon Marshall (Joint NYC 3-3-16)
- Euler systems for Rankin-Selberg convolutions and generalizations by Sarah Zerbes (Columbia 3-4-16)
- Higher regulators and non-critical values of degree 8 $L$-functions for GSp$(4) \times$ GL$(2)$ by Francesco Lemma (Columbia 3-25-16)
- Oddness of residually reducible Galois representations by Tobias Berger (Queens College 3-28-16)
- An automorphic version of the Deligne Conjecture by Jie Lin (Columbia 4-8-16)
- Distribution of rational points on some homogeneous varieties by Ramin Takloo-Bighash (Joint NYC 4-8-16)
- Generalized Heegner cycles and congruences of $p$-adic $L$-functions by Daniel Kriz (Columbia 4-15-16)
- On the integral kernel for a multiple Dirichlet series associated to Siegel cusp forms by Yves Martin (CUNY 5-13-16)
email: jimlb@g.clemson.edu | phone: 864-656-2331 | office: Long Hall 111 |