Title | With | Status | ||
---|---|---|---|---|
arXiv | Characteristic polynomials of p-adic matrices | Xavier Caruso, Tristan Vaccon | Submitted to ISSAC 2017 | |
arXiv | The dictionary for characters of smooth group schemes | Clifton Cunningham | Revising | |
arXiv | Division and slope factorization of p-adic polynomials | Xavier Caruso, Tristan Vaccon | Proceedings of the 2016 ACM on International Symposium on Symbolic and Algebraic Computation. ACM, New York, 2016, to appear. | |
arXiv | The canonical measure on a reductive p-adic group is motivic | Julia Gordon | Accepted by Annales scientifiques de l'École normale supérieure | |
arXiv | Quasicharacters and the function-sheaf dictionary | Clifton Cunningham | Accepted by the Journal of the Institute of Mathematics of Jussieu | |
arXiv | Rectifiers and the local Langlands correspondence: the unramified case | Moshe Adrian | Accepted by Mathematical Research Letters | |
arXiv | p-adic Stability in Linear Algebra | Xavier Caruso, Tristan Vaccon | Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation. ACM, New York, 2015, pp 101-108. | |
arXiv | Constructing local L-packets for tame unitary groups | |||
arXiv | The 3-adic eigencurve at the boundary of weight space | International Journal of Number Theory 10 (2014), no. 7, 1791-1806. | ||
arXiv | Tracking p-adic precision | Xavier Caruso, Tristan Vaccon | LMS Journal of Computation and Mathematics 17 (Special issue A) (2014), 274-294. | |
arXiv | Bounding Picard numbers of surfaces using p-adic cohomology | Timothy Abbott, Kiran Kedlaya | Arithmetic, Geometry and Coding Theory (AGCT 2005), Séminaires et Congrès 21, Societé Mathématique de France, 2009, 125-159. Magma source is available. |
Title | Notes | ||
---|---|---|---|
arXiv | The Local Langlands Correspondence for Tamely Ramified Groups | Ph.D. Thesis under Benedict Gross. Defended April 19, 2011 | |
arXiv | Formal Groups, Complex Cobordism and Quillen's Theorem | Minor thesis, a Ph.D. requirement at Harvard |
Please e-mail me to learn more about talks where I did not use slides.
Title | Dates | Venue | Paper | Description | |
---|---|---|---|---|---|
Using lattices to track p-adic precision | February 20, 2018 | Numerical Methods for Algebraic Curves | Lattice-based precision for p-adic computation. | ||
The inverse Galois problem for p-adic fields | November 13, 2017 | BU number theory seminar | |||
How to Win the Lottery | September 14, 2017 | Reed Colloquium | Talk on Cash Winfall, the lottery game that was actually profitable to play | ||
An introduction to p-adics in Sage | August 22, 2017 | Sage Days 88 | |||
p-adics in Sage | July 17, 2017 | Sage Days 87 | Introduction to Sage and p-adics. | ||
Makdisi's algorithm for Jacobians of p-adic curves | June 5, 2017 | Sage Days 86.5 | Application of p-adic precision to computing with divisors | ||
Computing with Modular Forms | May 22-26, 2017 | UNCG Summer School | Summer school on computational modular forms; I'm speaking on overconvergent modular symbols | ||
Modular Forms and Modular Symbols in Sage | February 8, 2017 | CLap-CLap | Introduction to using Sage for computations of modular forms | ||
Commutative Character Sheaves | December 2, 2016 | American University | arXiv | Talk on the new function-sheaf dictionary paper. | |
The Inverse Galois Problem for p-adic Fields | September 29, 2016 | University of Calgary Colloquium | Talk on algebraic tori database project | ||
Algebraic Tori and a Computational Inverse Galois Problem | September 17, 2016 | PANTS XXVI | Talk on algebraic tori database project | ||
Overcongergent Modular Symbols in Sage | March 20, 2016 | Sage Days 71 | Introduction to Overconvergent Modular Symbols in Sage | ||
Elliptic Curves, Triangles and L-functions | March 11, 2016 | Tufts University Colloquium | Colloquium on ranks of elliptic curves, the congruent number problem and the Birch and Swinnerton-Dyer conjecture | ||
Algebraic Tori and a Computational Inverse Galois Problem | January 26, 2016 | University of Pittsburgh | Talk on algebraic tori database project | ||
Overconvergent Modular Symbols in Sage | September 30, 2015 | RIMS Workshop on Computer Algebra Systems | Talk on Sage and Overconvergent Modular Symbols | ||
Positive slope pieces of the eigencurve via interpolation | July 30, 2015 | Computational Representation Theory in Number Theory | Talk on joint work with Ander Steele | ||
Positive slope pieces of the eigencurve via interpolation | May 28, 2015 | Explicit Methods for Abelian Varieties | Talk on joint work with Ander Steele | ||
A function-sheaf dictionary for tori over local fields | June 17, 2014 | CNTA XIII | arXiv | Talk on my function-sheaf dictionary paper | |
A function-sheaf dictionary for tori over local fields | May 24, 2014 | FRG on periods of automorphic forms and applications to L-functions | arXiv | Half-hour talk on my function-sheaf dictionary paper | |
Numerical Methods in p-adic Linear Algebra | February 3, 2014 | Lethbridge Number Theory and Combinatorics Seminar | arXiv | ||
A function-sheaf dictionary for tori over local fields | January 15, 2014 | Joint Mathematics Meetings 2014 | arXiv | Shorter talk on my work with Clifton | |
Quasicharacter Sheaves for Tori | December 5, 2013 | QVNTS | arXiv | Updated talk on my work with Clifton | |
Plans for p-adics in Sage | September 5, 2013 | Sage Days 52 | |||
Geometrizing Characters of Tori | June 24, 2013 | PRIMA 2013 | arXiv | Updated talk on my work with Clifton | |
Geometrizing Characters of Tori | May 12, 2013 | Alberta Number Theory Days 2013 | arXiv | Updated talk on my work with Clifton | |
Geometrizing Quasi-characters of Tori | January 28, 2013 | UCSC Number Theory Seminar | arXiv | Hour talk on my work with Clifton - some material has since been corrected | |
Geometrizing Quasi-characters of Tori | January 10, 2013 | Joint Mathematics Meetings 2013 | arXiv | 20 minute talk on my work with Clifton | |
The ABC Conjecture | November 16, 2012 | University of Calgary Colloquium | Sketch of Mochizuki's work | ||
Introduction to Sage | October 16, 2012 | University of Calgary - PMAT 621 | Most of the talk was this Sage notebook. | ||
The Local Langlands Correspondence and Character Sheaves | May 19, 2012 | Pacific Northwest Number Theory Conference 2012 | Similar to UW Number theory talk | ||
The Local Langlands Correspondence and Character Sheaves | May 17, 2012 | University of Washington Number Theory Seminar | Improved version of talk from Utah | ||
The Local Langlands Correspondence and Character Sheaves | April 26, 2012 | University of Utah number theory seminar | Thesis talk with a bit added on my work with Clifton | ||
Precision Models for Arithmetic in Local Fields | March 1, 2012 | UBC number theory seminar | arXiv | An improved version of my talk from Lyon in June | |
The State of p-Adics in Sage | February 19, 2012 | Sage Days 36 | |||
Coercions and Categories in Sage | January 26, 2012 | UW Sage Seminar | Sage notebook of this talk available here | ||
The Local Langlands Correspondence for Tamely Ramified Groups | December 8, 2011 | PIMS Number Theory Seminar | Thesis talk, extended to a 2 hour format | ||
Zeta Functions with p-Adic Cohomology | June 24, 2011 | Geocrypt 2011 | arXiv | A modified version of the talk I gave at CRM in April 2010 | |
Precision Models for Arithmetic in Local Fields | June 6, 2011 | Théorie de Hodge p-adique, équations différentielles p-adiques et leurs applications | arXiv | Talk on my work with Xavier Caruso | |
The Local Langlands Correspondence for Tamely Ramified Groups | February 9, 2011 | Harvard number theory seminar | Thesis talk, modified notes from my October 2010 talk. | ||
The Local Langlands Correspondence for Tamely Ramified Groups | January 20, 2011 | University of Calgary number theory seminar | Thesis talk, similar notes to my October 2010 talk. | ||
The Local Langlands Correspondence for Tamely Ramified Groups | December 1, 2010 | Universite Rennes Cryptography Seminar | Thesis talk, similar notes to my October 2010 talk. | ||
The Local Langlands Correspondence for Tamely Ramified Groups | October 2, 2010 | Quebec-Maine Number Theory 2010 | An overview of the Langlands correspondence for GL_n and an outline of my thesis work. | ||
Zeta Functions with p-adic cohomology | April 20, 2010 | Counting Points: Theory, Algorithms and Practice | arXiv | A presentation of the algorithm in my paper with Kiran and Tim. | |
Bruhat-Tits Theory | April 2, 9, 16, 2010 | Alcove Seminar | An overview of the Bruhat-Tits building. | ||
Coxeter Groups and 4-dimensional Polytopes | February 25, 2010 | Trivial Notions | Coxeter groups and classification of polytopes, together with Zome models of polyhedra and the 120-cell. | ||
Berkovich Spaces | April 29, 2009 | Alcove Seminar | An overview of Berkovich spaces. | ||
Weil Conjectures | February 26, 2009 | Trivial Notions | Weil conjectures and Weil cohomology theories for non-number theorists. | ||
Laplace to Langlands | Sept 25, Sept 30, Oct 2, 2008 | Alcove Seminar | A presentation on Gross's paper From Laplace to Langlands via representations of orthogonal groups. | ||
Embeddings of PSL_2(F_p) into semisimple linear algebraic groups | May 19, 2008 | STAGE | A presentation of the results in Serre's Exemples de plongements des groupes PSL_2(F_p) dans des groupes de Lie simples, Inventiones mathematicae, 1996. | ||
A Bound for the number of automorphisms of an arithmetic Riemann surface | April 10, 2008 | Trivial Notions | Based on the Arizona Winter School talk. | ||
A Bound for the number of automorphisms of an arithmetic Riemann surface | April 1, 2008 | UW Number Theory Seminar | Based on the Arizona Winter School talk. | ||
A Bound for the number of automorphisms of an arithmetic Riemann surface | March 19, 2008 | Arizona Winter School | Joint work with Linda Gruendken, Guillermo Mantilla, Dermot McCarthy, Kate Stange, Ying Zong, Maryna Viazovska. Based on Belolipetsky and Jones' paper of the same name. | ||
Representations de GL_2(Q_p) et (phi, Gamma)-modules | February 20, 27, March 5, 2008 | Taylor's Seminar | Talks on Colmez's paper of the same name. Joint talks with Ana Caraiani. List of results and index of notation: PDF. | ||
Eigenvarieties | December 10, 2007 | STAGE | A review based on Kevin Buzzard's lecture notes from the Eigenvarieties semester, which can be found here. | ||
p-Adic arithmetic in SAGE | September 30, 2007 | Sage Days 5 | Future directions for p-adic support in Sage. | ||
p-Adics in SAGE | June 14, 2007 | Sage Days 4 | Implementation notes for p-adics in Sage. | ||
Algorithms for p-adic polynomials and matrices | April 9, 2007 | STAGE | A discussion of some work of mine on algorithms for computing determinants and characteristic polynomials of p-adic matrices. I haven't written this material up yet. | ||
Sums of Squares Formulas | March 8, 2007 | Trivial Notions | Overview of the results in this paper of Dugger and Isaksen. | ||
Vanishing cycles in the analytic case | December 11, 2006 | Weil II seminar | Vanishing cycles and perverse sheaves as used in Deligne's proof of the Weil conjectures. | ||
The eigencurve near the boundary of weight space for p=2 and p=3 | November 13, 2006 | STAGE | arXiv | Presentation of a paper of Buzzard's and a followup paper of mine |
I use Kiran Kedlaya's list to find conferences. Number Theory Web is also useful.
A gold row indicates a conference that I organized, while a blue row indicates one where I spoke.
Dates | Year | Conference | Location |
---|---|---|---|
Sep 29-Oct 1 | 2017 | Open Source Computation and Algebraic Surfaces | BIRS, Banff, AB |
August 21-25 | 2017 | Sage Days 88 | IMA, Minneapolis, MN |
July 17-21 | 2017 | Sage Days 87 | UVM, Burlington, VT |
June 5-9 | 2017 | Sage Days 86.5 | Simon Frasier, Vancouver, BC |
May 22-26 | 2017 | UNCG Summer School on Computational Number Theory: Modular Forms | UNCG, Greensboro, NC |
February 6-10 | 2017 | CLap-CLap | Université Rennes 1, Rennes, France |
September 17-18 | 2016 | PANTS XXVI | UNCG, Greensboro, NC |
May 16-20 | 2016 | The p-adic Langlands Program and Related Topics | IU, Bloomington, IN |
May 9-13 | 2016 | AIM LMFDB Workshop | AIM, San Jose, CA |
March 25-28 | 2016 | Brisol LMFDB Workshop | Bristol, UK |
March 20-24 | 2016 | Explicit p-adic methods in number theory | Oxford, UK |
December 4-7 | 2015 | CMS Winter Meeting: Representation Theory | Montreal, QC |
Sep 30-Oct 2 | 2015 | Towards New Development of Mathematics via Computational Algebra Systems | RIMS, Kyoto, Japan |
July 27-31 | 2015 | Computational Representation Theory in Number Theory | OSU, Corvallis, OR |
May 25-29 | 2015 | Explicit Methods for Abelian Varieties | UC, Calgary, AB |
April 6-10 | 2015 | The Kudla Programme | CRM, Montreal, QC |
February 16-20 | 2015 | Regulators, Mahler measures, and special values of L-functions | CRM, Montreal, QC |
December 1-5 | 2014 | Motivic Integration, Orbital Integrals, and Zeta-Functions | BIRS, Banff, AB |
June 23-July 4 | 2014 | Counting Arithmetic Objects | CRM, Montreal, QC |
June 16-20 | 2014 | CNTA XIII | Carleton, Ottawa, ON |
June 2-6 | 2014 | p-adic variation in number theory | BU, Boston, MA |
May 23-25 | 2014 | Periods of automorphic forms and applications to L-functions | Harvard, Cambridge, MA |
May 19-23 | 2014 | Representations of Reductive Groups | MIT, Cambridge, MA |
April 18-20 | 2014 | Alberta Number Theory Days VI | BIRS, Banff, AB |
February 17-21 | 2014 | Hot Topics: Perfectoid Spaces and their Applications | MSRI, Berkeley, CA |
January 15-18 | 2014 | Joint Mathematics Meetings | Baltimore, MD |
December 6-9 | 2013 | CMS Winter Meeting | Ottawa, ON |
September 2-6 | 2013 | Sage Days 52 | Université Rennes 1, Rennes, France |
August 19-21 | 2013 | Workshop on Curves and Applications | UC, Calgary, AB |
June 24-28 | 2013 | PRIMA 2013 | Jiao Tong University, Shanghai, China |
May 10-12 | 2013 | Alberta Number Theory Days | BIRS, Banff, AB |
March 25-29 | 2013 | Sage Days 47 | PSU, Portland, OR |
Feb 26-Mar 2 | 2013 | Sage Days 46 | Oahu, HI |
Jan 31-Feb 3 | 2013 | Sage Days 44 | UW, Madison, WI |
January 9-12 | 2013 | Joint Mathematics Meetings | San Diego, CA |
December 7-10 | 2012 | CMS Winter Meeting | Montreal, QC |
May 24-29 | 2012 | Sage Days 40.5 | Wallace Falls, Seattle, WA |
May 19-21 | 2012 | Pacific Northwest Number Theory Conference | University of Idaho, Moscow, ID |
May 7-11 | 2012 | Geometrization of Smooth Characters | BIRS, Banff, AB |
Mar 24-Apr 1 | 2012 | LMFDB workshop | Bristol, UK |
March 11-16 | 2012 | Galois Representations, Shimura Varieties and Automorphic Forms | Fields Institute, Toronto, ON |
Febuary 19-23 | 2012 | Sage Days 36 | UCSD, La Jolla, CA |
September 15-18 | 2011 | Periods of Automorphic Forms and Applications to L-functions | Columbia, New York, NY |
June 26-July 1 | 2011 | L-packets | BIRS, Banff, AB |
June 18-22 | 2011 | GeoCrypt 2011 | Bastia, France |
June 6-9 | 2011 | Théorie de Hodge p-adique, équations différentielles p-adiques et leurs applications | Lyon, France |
October 2-3 | 2010 | Quebec-Maine Number Theory Conference | Université Laval, Quebec City, QC |
June 2-5 | 2010 | Number Theory and Representation Theory: Dick Gross' 60th Birthday Conference | Harvard, Cambridge, MA |
April 19-23 | 2010 | Counting Points: Theory, Algorithms and Practice | CRM, Montreal, QC |
December 1-4 | 2009 | Sage Days 18 | CMI, Cambridge, MA |
May 16-21 | 2009 | Sage Days 15 | UW, Seattle, WA |
Mar 29-Apr 7 | 2009 | p-Adic Methods in Arithmetic Algebraic Geometry | Hebrew University, Jerusalem, Israel |
March 13-19 | 2009 | Arizona Winter School: Quadratic Forms | UA, Tucson, AZ |
January 20-25 | 2009 | Sage Days 12 | UCSD, San Diego, CA |
June 23-27 | 2008 | LMFDB Workshop | UW, Seattle, WA |
June 9-20 | 2008 | Sage Devel Days 1 | UW, Seattle, WA |
February 5-9 | 2008 | Sage Days 7 | IPAM, Los Angeles, CA |
November 10-14 | 2007 | Sage Days 6 | Bristol, UK |
Sep 30-Oct 3 | 2007 | Sage Days 5 | CMI, Cambridge, MA |
June 12-17 | 2007 | Sage Days 4 | UW, Seattle, WA |
February 17-21 | 2007 | Sage Days 3 | IPAM, Los Angeles, CA |
October 6-10 | 2006 | Sage Days 2 | UW, Seattle, WA |
February 4-5 | 2006 | Sage Days 1 | UCSD, San Diego, CA |
Degree | Subject | University | Completed |
---|---|---|---|
Doctor of Philosophy | Mathematics | Harvard University | 2011 |
Bachelor of Science | Mathematics | Massachusetts Institute of Technology | 2006 |
Bachelor of Science | Literature | Massachusetts Institute of Technology | 2006 |
Position | University | Duration |
---|---|---|
Postdoctoral Fellow | University of Pittsburgh | 2015-present |
Postdoctoral Fellow | University of British Columbia | 2014-2015 |
Postdoctoral Fellow | University of Calgary | 2011-2014 |
PIMS Postdoctoral Fellowship | 2011 |
National Defense Science and Engineering Graduate Fellowship | 2006 |
NSF Graduate Research Fellowship | 2006 |
Phi Beta Kappa member | 2006 |
Todd Anderson award for excellent teaching at ESG | 2006 |
Rogers Prize for undergraduate research at SPUR | 2004 |
National Merit Scholar | 2002 |
Course | Institution | Role | Semesters | |
---|---|---|---|---|
Math 430 | Introduction to Abstract Algebraic Systems | University of Pittsburgh | Instructor | Fall 2017 |
Math 220 | Analytic Geometry & Calculus 1 | University of Pittsburgh | Lecturer | Fall 2017 |
Math 240 | Analytic Geometry & Calculus 3 | University of Pittsburgh | Lecturer | Spring 2017 |
Math 220 | Analytic Geometry & Calculus 1 | University of Pittsburgh | Lecturer | Fall 2016 |
Math 430 | Introduction to Abstract Algebraic Systems | University of Pittsburgh | Instructor | Spring 2016 |
Math 220 | Analytic Geometry & Calculus 1 | University of Pittsburgh | Lecturer | Fall 2015 |
Math 200 | Multivariable Calculus | University of British Columbia | Lecturer | Fall 2014 |
Math 211 | Linear Methods | University of Calgary | Lecturer | Fall 2013 |
PMAT 527/627 | Computational Number Theory | University of Calgary | Instructor | Fall 2012 |
Math 223a | Algebraic Number Theory | Harvard University | Course assistant | Fall 2008 |
QR 28 | Magic of Numbers | Harvard University | Teaching fellow | Fall 2008 |
18.821 | Project Lab in Mathematics | Massachusetts Institute of Technology | Teaching assistant | Spring 2006 |
18.02 | Multivariable Calculus | Experimental Study Group at MIT | Instructor | Fall 2003, Spring 2005, Fall 2005 |
Many short courses | Canada/USA Mathcamp | Counselor | Summers 2003, 2006-2009, 2011, 2016 |
Conference | With | Budget | Dates |
---|---|---|---|
Sage Days 87 | Jen Balakrishnan, Xavier Caruso, Edgar Costa, Taylor Dupuy, William Stein, Christelle Vincent | $47K | July 17-22, 2017 |
Explicit p-adic methods in number theory | Jen Balakrishnan | $36K | March 20-24, 2016 |
CMS Winter Session: Representation Theory | Clifton Cunningham | None | December 4-7, 2015 |
Alberta Number Theory Days | Brandon Fodden | $10K | May 10-12, 2013 |
Sage Days 44 | Rob Harron, William Stein | $10K | January 31-February 3, 2013 |
Sage Days 40.5 | William Stein | $10K | May 24-29, 2012 |
Sage Days 36 | Kiran Kedlaya, William Stein | $30K | February 19-23, 2012 |
Academic Coordinator for Mathcamp 2016 | Canada/USA Mathcamp | Summer 2016 |
Organizer of the Number theory video seminar | University of British Columbia | Fall 2014 |
Organizer of the ABC seminar | University of Calgary | Fall 2012 |
Organizer of the Alcove seminar | Harvard University | 2008-2011 |
Developer for the Sage project | 2006-present | |
Volunteer teacher at Splash | Massachusetts Institute of Technology | 2002-2009 |
Coach of two MATHCOUNTS teams | Catlin Gabel School, West Sylvan Middle School | 1998-2002 |
I am interested in explicit computation of L-packets, following DeBacker and Reeder.
I am interested in practical algorithms involving p-adic numbers.
I maintain homepages for the following courses, past and present.
Course | Institution | Semester |
---|---|---|
Math 430 - Introduction to Abstract Algebraic Systems | University of Pittsburgh | Fall 2017 |
Math 220 - Calculus 1 | University of Pittsburgh | Fall 2017 |
Math 240 - Calculus 3 | University of Pittsburgh | Spring 2017 |
Math 220 - Calculus 1 | University of Pittsburgh | Fall 2016 |
Math 400 - Discrete Mathematical Structures | University of Pittsburgh | Fall 2016 |
Math 430 - Introduction to Abstract Algebraic Systems | University of Pittsburgh | Spring 2016 |
Math 220 - Calculus 1 | University of Pittsburgh | Fall 2015 |
Math 200 - Multivariable Calculus | University of British Columbia | Fall 2014 |
Math 211 - Linear Methods | University of Calgary | Fall 2013 |
PMAT 627 - Computational Number Theory | University of Calgary | Fall 2012 |
QR 28 - Magic of Numbers | Harvard University | Fall 2008 |
18.02 - Multivariable Calculus | Experimental Study Group at MIT | Fall 2005 |
18.02 - Multivariable Calculus | Experimental Study Group at MIT | Spring 2005 |
This page is aimed at my students who are looking for resources beyond the textbook and homework problems.
While calculators and computers are not allowed on exams, learning to use them effectively will aid you in your applications of calculus in the future. See this list of math software packages to get started. I help develop Sage, and recommend it in particular.
There are many resources for learning calculus online. Here is a sample, but you should explore on your own!
The best way to reach me is by e-mail.
Department of Mathematics
University of Pittsburgh
301 Thackeray Hall
Pittsburgh, PA 15260
426 Thackeray Hall
TR 2-3:45pm
Other times available by arrangement if you cannot make either of these.