Articles

Title With Status
PDF arXiv Characteristic polynomials of p-adic matrices Xavier Caruso, Tristan Vaccon Submitted to ISSAC 2017
PDF arXiv The dictionary for characters of smooth group schemes Clifton Cunningham Revising for the Canadian Journal of Mathematics
PDF 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.
PDF arXiv The canonical measure on a reductive p-adic group is motivic Julia Gordon Accepted by Annales scientifiques de l'École normale supérieure
PDF arXiv Quasicharacters and the function-sheaf dictionary Clifton Cunningham Accepted by the Journal of the Institute of Mathematics of Jussieu
PDF arXiv Rectifiers and the local Langlands correspondence: the unramified case Moshe Adrian Accepted by Mathematical Research Letters
PDF 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.
PDF arXiv Constructing local L-packets for tame unitary groups
PDF arXiv The 3-adic eigencurve at the boundary of weight space International Journal of Number Theory 10 (2014), no. 7, 1791-1806.
PDF arXiv Tracking p-adic precision Xavier Caruso, Tristan Vaccon LMS Journal of Computation and Mathematics 17 (Special issue A) (2014), 274-294.
PDF 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.

Theses

Title Notes
PDF arXiv The Local Langlands Correspondence for Tamely Ramified Groups Ph.D. Thesis under Benedict Gross. Defended April 19, 2011
PDF arXiv Formal Groups, Complex Cobordism and Quillen's Theorem Minor thesis, a Ph.D. requirement at Harvard

Talks

Please e-mail me to learn more about talks where I did not use slides.

Title Dates Venue Paper Description
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
PDF 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
PDF Algebraic Tori and a Computational Inverse Galois Problem January 26, 2016 University of Pittsburgh Talk on algebraic tori database project
PDF 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
PDF A function-sheaf dictionary for tori over local fields June 17, 2014 CNTA XIII arXiv Talk on my function-sheaf dictionary paper
PDF 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
PDF Numerical Methods in p-adic Linear Algebra February 3, 2014 Lethbridge Number Theory and Combinatorics Seminar arXiv
PDF A function-sheaf dictionary for tori over local fields January 15, 2014 Joint Mathematics Meetings 2014 arXiv Shorter talk on my work with Clifton
PDF Quasicharacter Sheaves for Tori December 5, 2013 QVNTS arXiv Updated talk on my work with Clifton
PDF Plans for p-adics in Sage September 5, 2013 Sage Days 52
PDF Geometrizing Characters of Tori June 24, 2013 PRIMA 2013 arXiv Updated talk on my work with Clifton
PDF Geometrizing Characters of Tori May 12, 2013 Alberta Number Theory Days 2013 arXiv Updated talk on my work with Clifton
PDF 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
PDF Geometrizing Quasi-characters of Tori January 10, 2013 Joint Mathematics Meetings 2013 arXiv 20 minute talk on my work with Clifton
PDF The ABC Conjecture November 16, 2012 University of Calgary Colloquium Sketch of Mochizuki's work
PDF Introduction to Sage October 16, 2012 University of Calgary - PMAT 621 Most of the talk was this Sage notebook.
PDF The Local Langlands Correspondence and Character Sheaves May 19, 2012 Pacific Northwest Number Theory Conference 2012 PDF Similar to UW Number theory talk
PDF The Local Langlands Correspondence and Character Sheaves May 17, 2012 University of Washington Number Theory Seminar PDF Improved version of talk from Utah
PDF The Local Langlands Correspondence and Character Sheaves April 26, 2012 University of Utah number theory seminar PDF Thesis talk with a bit added on my work with Clifton
PDF 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
PDF The Local Langlands Correspondence for Tamely Ramified Groups December 8, 2011 PIMS Number Theory Seminar PDF Thesis talk, extended to a 2 hour format
PDF 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
PDF 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
PDF The Local Langlands Correspondence for Tamely Ramified Groups February 9, 2011 Harvard number theory seminar PDF 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 PDF Thesis talk, similar notes to my October 2010 talk.
The Local Langlands Correspondence for Tamely Ramified Groups December 1, 2010 Universite Rennes Cryptography Seminar PDF Thesis talk, similar notes to my October 2010 talk.
PDF The Local Langlands Correspondence for Tamely Ramified Groups October 2, 2010 Quebec-Maine Number Theory 2010 PDF An overview of the Langlands correspondence for GL_n and an outline of my thesis work.
PDF 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.
PDF 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.
PDF 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.
PDF 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.
PDF p-Adic arithmetic in SAGE September 30, 2007 Sage Days 5 Future directions for p-adic support in Sage.
PDF 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

Conferences

I use Kiran Kedlaya's list to find conferences. Number Theory Web is also useful.

Past and Future Conferences Attended

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 12017Open Source Computation and Algebraic SurfacesBIRS, Banff, AB
August 21-252017Sage Days 88IMA, Minneapolis, MN
July 17-212017Sage Days 87UVM, Burlington, VT
June 5-92017Sage Days 86.5Simon Frasier, Vancouver, BC
May 22-262017UNCG Summer School on Computational Number Theory: Modular FormsUNCG, Greensboro, NC
February 6-102017CLap-CLapUniversité Rennes 1, Rennes, France
September 17-182016PANTS XXVIUNCG, Greensboro, NC
May 16-202016The p-adic Langlands Program and Related TopicsIU, Bloomington, IN
May 9-132016AIM LMFDB WorkshopAIM, San Jose, CA
March 25-282016Brisol LMFDB WorkshopBristol, UK
March 20-242016Explicit p-adic methods in number theoryOxford, UK
December 4-72015CMS Winter Meeting: Representation TheoryMontreal, QC
Sep 30-Oct 22015Towards New Development of Mathematics via Computational Algebra SystemsRIMS, Kyoto, Japan
July 27-312015Computational Representation Theory in Number TheoryOSU, Corvallis, OR
May 25-292015Explicit Methods for Abelian VarietiesUC, Calgary, AB
April 6-102015The Kudla ProgrammeCRM, Montreal, QC
February 16-202015Regulators, Mahler measures, and special values of L-functionsCRM, Montreal, QC
December 1-52014Motivic Integration, Orbital Integrals, and Zeta-FunctionsBIRS, Banff, AB
June 23-July 42014Counting Arithmetic ObjectsCRM, Montreal, QC
June 16-202014CNTA XIIICarleton, Ottawa, ON
June 2-62014p-adic variation in number theoryBU, Boston, MA
May 23-252014Periods of automorphic forms and applications to L-functionsHarvard, Cambridge, MA
May 19-232014Representations of Reductive GroupsMIT, Cambridge, MA
April 18-202014Alberta Number Theory Days VIBIRS, Banff, AB
February 17-212014Hot Topics: Perfectoid Spaces and their ApplicationsMSRI, Berkeley, CA
January 15-182014Joint Mathematics MeetingsBaltimore, MD
December 6-92013CMS Winter MeetingOttawa, ON
September 2-62013Sage Days 52Université Rennes 1, Rennes, France
August 19-212013Workshop on Curves and ApplicationsUC, Calgary, AB
June 24-282013PRIMA 2013Jiao Tong University, Shanghai, China
May 10-122013Alberta Number Theory DaysBIRS, Banff, AB
March 25-292013Sage Days 47PSU, Portland, OR
Feb 26-Mar 22013Sage Days 46Oahu, HI
Jan 31-Feb 32013Sage Days 44UW, Madison, WI
January 9-122013Joint Mathematics MeetingsSan Diego, CA
December 7-102012CMS Winter MeetingMontreal, QC
May 24-292012Sage Days 40.5Wallace Falls, Seattle, WA
May 19-212012Pacific Northwest Number Theory ConferenceUniversity of Idaho, Moscow, ID
May 7-112012Geometrization of Smooth CharactersBIRS, Banff, AB
Mar 24-Apr 12012LMFDB workshopBristol, UK
March 11-162012Galois Representations, Shimura Varieties and Automorphic FormsFields Institute, Toronto, ON
Febuary 19-232012Sage Days 36UCSD, La Jolla, CA
September 15-182011Periods of Automorphic Forms and Applications to L-functionsColumbia, New York, NY
June 26-July 12011L-packetsBIRS, Banff, AB
June 18-222011GeoCrypt 2011Bastia, France
June 6-92011Théorie de Hodge p-adique, équations différentielles p-adiques et leurs applications Lyon, France
October 2-32010Quebec-Maine Number Theory ConferenceUniversité Laval, Quebec City, QC
June 2-52010Number Theory and Representation Theory: Dick Gross' 60th Birthday ConferenceHarvard, Cambridge, MA
April 19-232010Counting Points: Theory, Algorithms and PracticeCRM, Montreal, QC
December 1-42009Sage Days 18CMI, Cambridge, MA
May 16-212009Sage Days 15UW, Seattle, WA
Mar 29-Apr 72009p-Adic Methods in Arithmetic Algebraic GeometryHebrew University, Jerusalem, Israel
March 13-192009Arizona Winter School: Quadratic FormsUA, Tucson, AZ
January 20-252009Sage Days 12UCSD, San Diego, CA
June 23-272008LMFDB WorkshopUW, Seattle, WA
June 9-202008Sage Devel Days 1UW, Seattle, WA
February 5-92008Sage Days 7IPAM, Los Angeles, CA
November 10-142007Sage Days 6Bristol, UK
Sep 30-Oct 32007Sage Days 5CMI, Cambridge, MA
June 12-172007Sage Days 4UW, Seattle, WA
February 17-212007Sage Days 3IPAM, Los Angeles, CA
October 6-102006Sage Days 2UW, Seattle, WA
February 4-52006Sage Days 1UCSD, San Diego, CA

Curriculum Vitae   PDF

Education

Degree Subject University Completed
Doctor of Philosophy Mathematics Harvard 2011
Bachelor of Science Mathematics 2006
Bachelor of Science Literature 2006

Employment

Position University Duration
Postdoctoral Fellow 2015-present
Postdoctoral Fellow 2014-2015
Postdoctoral Fellow Calgary 2011-2014

Honors and Awards

Publications

Talks

Teaching Experience

Course Institution Role Semesters
Math 430 Introduction to Abstract Algebraic Systems Instructor Fall 2017
Math 220 Analytic Geometry & Calculus 1 Lecturer Fall 2017
Math 240 Analytic Geometry & Calculus 3 Lecturer Spring 2017
Math 220 Analytic Geometry & Calculus 1 Lecturer Fall 2016
Math 430 Introduction to Abstract Algebraic Systems Instructor Spring 2016
Math 220 Analytic Geometry & Calculus 1 Lecturer Fall 2015
Math 200 Multivariable Calculus Lecturer Fall 2014
Math 211 Linear Methods Calgary Lecturer Fall 2013
PMAT 527/627 Computational Number Theory Calgary Instructor Fall 2012
Math 223a Algebraic Number Theory Harvard Course assistant Fall 2008
QR 28 Magic of Numbers Harvard Teaching fellow Fall 2008
18.821 Project Lab in Mathematics Teaching assistant Spring 2006
18.02 Multivariable Calculus Instructor Fall 2003, Spring 2005, Fall 2005
Many short courses Mathcamp Counselor Summers 2003, 2006-2009, 2011, 2016

Conferences Organized

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

Other Activities

Academic Coordinator for Mathcamp 2016 Mathcamp Summer 2016
Organizer of the Number theory video seminar Fall 2014
Organizer of the ABC seminar Calgary Fall 2012
Organizer of the Alcove seminar Harvard 2008-2011
Developer for the Sage project 2006-present
Volunteer teacher at Splash 2002-2009
Coach of two MATHCOUNTS teams Catlin Gabel , West Sylvan 1998-2002

Interests   PDF

The local Langlands correspondence

I am interested in explicit computation of L-packets, following DeBacker and Reeder.

p-adic Computation

I am interested in practical algorithms involving p-adic numbers.

Resources

This page is aimed at my students who are looking for resources beyond the textbook and homework problems.

Help at Pitt

  • Your TA is there to answer your questions and help you understand the material. If you are struggling, you should definitely be going to recitation.
  • The Math Assitance Center is open about 10 hours a day on weekdays, with graduate TAs available to answer questions.
  • The Calculus/Engineering Computer Lab has a posted schedule where TAs are able to help with questions on your online assignments.
  • The Academic Resource Center has programs for finding tutors and learning study and time-management skills.
  • Sometimes life interferes with school. If you're struggling with mental health, I encourage you to get help, either at Pitt's Counseling Center or elsewhere.

Software

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.

Online

There are many resources for learning calculus online. Here is a sample, but you should explore on your own!

  • MIT's OpenCourseWare offers videos, textbooks and courses which can provide a different perspective on a topic you might be struggling with.
  • Sage's Calculus Tutorial mixes calculus and Sage.
  • CALCULUS.ORG offers a lengthy list of calculus related sites, including the two above.
  • Math Stack Exchange is a question and answer site aimed at calculus and beyond.

Contact Info

The best way to reach me is by e-mail.

E-mail

roed@pitt.edu

Mailing Address

Department of Mathematics
University of Pittsburgh
301 Thackeray Hall
Pittsburgh, PA 15260

Office Hours

426 Thackeray Hall
MW 4-5:15pm
M 9-10pm with advance notice
Other times available by arrangement if you cannot make any of these.