GUILLERMO MANTILLA-SOLER
Department of Mathematics +(571) 3394949 Ext 5220
Universidad de los Andes [email protected]
Bogot´a, Colombia. matematicas.uniandes.edu.co/∼gmantilla
Employment
Universidad de los Andes Bogot´a, Colombia
Assistant Professor(TT)
2014-´
Ecole F´ed´erale Polytechnique de Lausanne Lausanne, Switzerland
Postdoctoral research fellow 2012-2014
Mentor: Eva Bayer-Fluckiger
University of British Columbia Vancouver, BC, Canada
Postdoctoral research fellow 2010-2012
Mentor: Nike Vatsal
Education
University of Wisconsin-Madison Madison, Wisconsin, USA
Ph.D. in Mathematics. 2010
M.A. in Mathematics 2006
• Advisor Jordan S. Ellenberg
Universidad de los Andes Bogot´a, Colombia
M.S. in Mathematics 2005
B.S. in Mathematics 2002
• Advisor Xavier F. Caicedo
Research interests
• Active interests: Algebraic number theory(Invariants of number fields, integral trace forms, Dedekind zeta functions), Arithmetic algebraic geometry(Iwasawa theory, Galois representations).
• Other: Commutative algebra, Applications of model theory to algebra.
Research, preprints and publications
• The shape ofZ/`Z-number fields. With M. Monsurr`o. Ramanujan Journal DOI: 10.1007/s11139-015-9744-2
• The spinor genus of the integral trace form. Transactions of the American Mathematical Society DOI: 10.1090/tran/6723
• On the Arithmetic determination of the trace. Journal of Algebra (2015) Vol 444, 272-283.
• Weak arithmetic equivalence. Canadian Mathematical Bulletin (2015) Vol 58 no 1, 115-127.
• A space of weight 1modular forms attached to totally real cubic number fields. Contemporary Mathematics 649,trends in number theory, (2015), 131-137.
• On number fields with equivalent integral trace forms. International Journal of Number Theory 8 (2012), no, 7, 1569-1580.
• Power map permutations and symmetric differences on finite groups. Joint work with M´arton Hablicsek. Journal of Algebra and its applications 10 (2011), no, 5, 947-959.
• Integral trace forms associated to cubic extensions. Algebra and Number Theory 4 (2010), no, 6, 681-699.
• Mordell-Weil ranks in towers of modular Jacobians. Ph.D thesis.
• Automorfismos polinomiales y la conjetura de Keller. Sponsored by the Research Fund of the Science Faculty, Universidad de Los Andes. 2005
Teaching experience
• Algebra II/Galois theory, Second course in linear algebra, Algebraic number theory. Universidad de los Andes, 2014-.
• Assistant to Eva Bayer Fluckiger for Algebra I, II at EPFL. 2012-2014.
• Conducting a learning seminar on classic Iwasawa theory for Graduate students at UBC. Fall 2011.
• Instructor for Matrix algebra, Integral and differential calculus at UBC. 2010-2011.
• Instructor, Summer Enhancement Program in Algebra 2008, 2009 and 2010. This class is for graduate students in the Math department(Students in the class are usually at the beginning of their 1st, 2nd or 3d year). Seehttp://matematicas.uniandes.edu.co/~gmantilla/Teaching/SEP.htmfor more information about SEP.
• Teaching Assistant for Linear Algebra, Calculus I, II, III and Business Calculus. University of Wisconsin, Madison, WI August 2005-2010.
• Teaching Assistant for Calculus III, ODE’S, Numerical Analysis. Universidad de los Andes, Bogot´a, Colombia, January 2001-May 2005.
• Lecturer, Calculus I,II, Linear Algebra and Discrete Math. Universidad de los Andes, Bogot´a, Colombia, January 2001-May 2005.
• Lecturer, Business Mathematics. Universidad del Rosario, Bogot´a, Colombia, January 2004-May 2004.
• Instructor, Algebra Summer Course. Colegio San Carlos, Bogot´a, Colombia, Summer 2001.
Students supervised.
Ongoing• Lu´ıs Felipe Vargas. Undergraduate, Universidad de los Andes.
• Jerson Caro Reyes. Master, Universidad de los Andes.
• Wilmar Reinerio. Ph.D, Universidad de los Andes.
• Juanita Duque Rosero. Undergraduate, Universidad de los Andes.
• Santiago Arango. Undergraduate, Universidad de los Andes.
• Santiago Cort´es. Undergraduate, Universidad de los Andes. Finished projects
• Approche alg´ebrique du th´or`eme de la progression arithm´etique de Dirichlet by Ga¨uetan Gogniat. Third year year project at EPFL co-supervised by Eva Bayer-Fluckiger. Spring 2014.
• An elementary proof of the fundamental theorem of algebraby Filip Fifka. Second year project at EPFL , co-supervised by Eva Bayer-Fluckiger. Spring 2014.
• Sur la transcendance de πet le th´or`eme de Lindemann-Weierstrassby Philippe Atten. Fourth year project at EPFL co-supervised by Eva Bayer-Fluckiger. Fall 2013.
• Les nombresp-adiquesby Erwan kohler. Third year project at EPFL co-supervised by Eva Bayer-Fluckiger. May 2013.
Talks
Research talks
• Invited speaker, CMS Winter meeting, Special Session on algebraic number theory. Montreal, Canada, December 2015.
• Invited Speaker, 29th Journ´ees Arithm´etiques, Debrecen, Hungary, July 2015.
• Invited Speaker, Sextas Jornadas en Teor´ıa de n´umeros, Valladolid, Spain, July 2015.
• Invited speaker, AMS Special Session on quadratic forms in Arithmetic and Geometry. UAH, Huntsville, AL, March 2015.
• Invited Speaker, ICM 2014 satellite conference on integral quadratic forms and related topics. Gyeongju, South Korea, August 2014.
• Speaker at S´eminaire d’Alg`ebre et de Th´eorie des Nombres, EPFL, Switzerland, July 2014.
• Invited Speaker, S´eminaire de Th´eorie des Nombres, Institute de Math´ematiques de Bordeaux, France, April 2014.
• Invited Speaker, joint PIMS/SFU/UBC Number theory seminar, BC, Canada, January 2014.
• Speaker, joint meetings of the AMS, Baltimore, MD, USA, January 2014.
• Invited Speaker, Atelier pro-p-groupes et arithm´etique , Laboratoire de math´ematiques de Besan¸con, France, December 2013.
• Invited Speaker, Algebra, geometry and number theory seminar, Universiteit Leiden, Netherlands, November 2013.
• Invited Speaker, Colloquium, Universit´e de Neuchˆatel, Switzerland, October 2013.
• Invited Speaker, Emory Algebra and Number Theory Seminar, Atlanta, GA, September 2013.
• Invited Speaker, Qu´ebec-Vermont number theory seminar, Montreal, Canada, September 2013.
• Invited Speaker, Algebra seminar University of Western Ontario. London, Canada, September 2013.
• Invited Speaker, Number theory seminar, University of Wisconsin, Madison, September 2013.
• Invited Speaker, Number theory seminar, University of South Carolina, Columbia, August 2013.
• Invited Speaker, Quintas Jornadas en Teor´ıa de n´umeros, Seville, Spain, July 2013.
• Invited Speaker, 28th Journ´ees Arithm´etiques, Grenoble, France, July 2013.
• Invited Speaker, Seminario di Geometria Algebrica, Universit´a Europea di Roma, Italy, June 2013.
• Invited Speaker, S´eminaire de Th´eorie des Nombres Universit´e Blaise Pascal, Clermont-Ferrand, France, May 2013.
• Invited Speaker, Universidad Sergio Arboleda, Bogot´a, Colombia, February 2013..
• Invited Speaker, Seminario de ´Algebra Universidad de Los Andes, Bogot´a, Colombia, February 2013.
• Invited Speaker, S´eminaire d’Alg`ebre et de Th´eorie des Nombres, Laboratoire de math´ematiques de Besan¸con, France, February 2013.
• Invited Speaker, Algebra and combinatorics seminar, Aalto University, Helsinki, Finland, December 2012.
• Invited speaker, 25th Automorphic forms workshop. Oregon state University, Corvallis, OR, March 2011
• Speaker at the joint PIMS/SFU/UBC Number theory seminar. Vancouver, Canada, February, 2011.
• Invited speaker, CMS Special Session onp-adic groups, Automorphic forms and Geometry. Vancouver, Canada, December 2010.
• Speaker at the joint PIMS/SFU/UBC Number theory seminar. Vancouver, Canada, November 2010.
• Invited speaker, Joint meeting special session Arithmetic Geometry. San Francisco, CA, January 2010.
• Invited speaker, AMS Special Session on Arithmetic and profinite groups. Penn State, State College, PA, October 2009.
• Invited speaker, Algebra seminar University of Western Ontario. London, Canada, March 2009.
• Invited speaker, Conference on Quadratic Forms, Sums of Squares, Theta Functions and Integral Lattices. University of Florida, Gainesville, FL, March 2009.
• Invited speaker, AMS Special Session on Number Theory and Applications in Other Fields. LSU, Baton Rouge, LA, March 2008.
Mini-courses
• Una introducci´on a las representaciones de Galois y a la teor´ıa de Iwasawa. Universidad de los Andes, Bogot´a, Colombia, 2015.
• El ´ultimo teorema de Fermat. Main speaker for a two week workshop on FLT. Universidad de Antioquia, Medell´ın, Colombia, 2015.
• Quadratic forms in number theory. CUSO Doctoral School, Les Diablerets, Switzerland, March 2014.
• El principio de Hasse, Taller en teor´ıa de n´umeros. Universidad de los Andes, Bogot´a, Colombia, October 2008.
Expository talks
• Formas cuadr´aticas racionales y el principio global vs local. Conferencista invitado a la tercera escuela de Matem´aticas, Universidad los Libertadores, Bogot´a, Colombia, May 2015.
• Cohomological invariants–InvK(c2, c2). Algebraic group seminar, UBC, Vancouver, Canada, March 2012.
• Hochschild-Serre, and Grothendieck spectral sequences. Algebraic group seminar, UBC, Vancouver, Canada, April 2011.
• Jet spaces and the motivic measure. Motivic integration seminar, UBC, Vancouver, Canada, January 2011.
• ´etale group schemes. Postdoc seminars, UBC, Vancouver, Canada, October 2010.
• Quadratic reciprocity in finite groups. Group theory seminar, UW Madison. Madison, WI, September 2009.
• Galois Coverings, Encuentro en geometr´ıa y topolog´ıa de acciones de grupos. Universidad de los Andes, Bogot´a, Colombia, May 2009.
• Galois representations. Number theory seminar UW Madison. Madison, WI March 2009.
• Arithmetically equivalent number fields. Number theory seminar, UW Madison. Madison, WI, November 2008.
• Automorphisms of Arithmetic Riemann Surfaces. A bound for the number of automorphisms of an arithmetic Riemann surfaces. Arizona Winter School, University of Arizona, Tucson, AZ, March 2008.
• Rudiments of Iwasawa theory: the completed group algebra ofZp and class groups of number fields. Group
theory seminar, UW Madison Madison, WI, October 2007.
• Students presentation, Ralph Greenberg’s project. Summer School in Iwasawa Theory, Fields Institute. Hamilton, ON, August 2007.
• Group Schemes. Reading seminar on Fermat’s last theorem at UW Madison. Madison, WI, November 2006.
• Local Fields and Elliptic Curves over Local Fields. Number theory seminar, UW Madison. Madison, WI, October 2006.
• Sistemas de raices en algebras de Lie.Universidad de los Andes, Bogot´a, Colombia, March 2005.
• El ´ındice como Morfismo de Monoides definido sobre los Operadores de Fredholm. Universidad de los Andes, Bogot´a, Colombia, November 2003.
• Compact and Fredholm Operators and Notion of Index. Geometric and Topological Methods for Quantum Field Theory, Villa de Leyva, Colombia, July 2003.
• Dominios de Ideales Principales no Euclidianos y Extensiones Quadraticas de los Racionales. Universidad de los Andes, Bogot´a, Colombia, June 2003.
• El problema de integracion de funciones elementales en Terminos finitos. Universidad de los Andes, Bogot´a, Colombia, November 2002.
• Extensions of Operators by Ultrapowers Segunda escuela Matematica de America Latina y el Caribe. Merida, Venezuela, September 2002.
Academic service and Memberships
• Member of the American Mathematical Society
• Member of the Sociedad Colombiana de Matem´aticas
• Organizer of the Mathematics Colloquium, Universidad de los Andes. January 2015–
• Library coordinator of the Mathematics department, Universidad de los Andes. January 2015–
• Co-organizer of Swiss Doctoral Program in Mathematics March, Kervaire Seminar,Quadratic forms and Applications. Les Diablerets, Switzerland, March 2014.
• Organizer 26th Automorphic forms workshop. University of British Columbia, Vancouver, BC, April 2012.
• Referee/Review work: Proceedings of the American Mathematical Society, Algebra & Number Theory, International Journal of Number Theory, Mathematical Reviews.
• Grader for Graduate classes in Elliptic Curves and modular forms (under the supervision of Jordan Ellenberg), Algebraic Number Theory (under the supervision of Amanda Folsom) and analytical number theory (under the supervision of Riad Masri).
• Organizer, Midwest Number Theory conference for Graduate students V. University of Wisconsin, Madison, WI, November 2007.
• Member of the Committee of the Colombian olympiad of university Mathematics.(In charge of designing and grade classificatory and final rounds of competitions.) Colombian Mathematical Olympiad, Bogot´a,
Colombia, January 2004-July 2005.
Distinctions
• My grant proposals for the organization of the 26th AFW, held in Vancouver in 2012, were accepted with a total of $5000US from the Number theory foundation and $8000CA from the Pacific Institute for the Mathematical sciences.
• Invited speaker by the Centre for Teaching, Learning and Technology (CTLT) at UBC to talk to new faculty hires about my experiences as a successful teacher at UBC. September 2011.
• Math Department excellence in teaching award at UW Madison. October 2009.
• Awarded Vilas Travel Grant to participate in the 2010 Joint meetings of the AMS. December 2009.
• 29th Journ´ees Arithm´etiques, Debrecen, Hungary, July 2015.
• Sextas Jornadas en Teor´ıa de n´umeros, Valladolid, Spain, July 2015.
• Counting arithmetic objects(Ranks of elliptic curves), Montreal, Canada, November 2014.
• Quintas Jornadas en Teor´ıa de n´umeros, Seville, Spain, July 2013.
• 28th Journ´ees Arithm´etiques, Grenoble, France, July 2013.
• Seminario di Geometria Algebrica, Universit´a Europea di Roma, Italy, June 2013.
• Arithmetic of abelian varieties in families, Lausanne, CH, November 2012.
• Contemporary methods for solving Diophantine equations, Banff, Alberta, CA, June 2012.
• 26th Automorphic forms workshop. University of British Columbia, Vancouver, BC, April 2012.
• Diophantine methods, lattices, and arithmetic theory of quadratic forms, Banff, Alberta, CA, November 2011.
• Instructional workshop on the noncommutative main conjectures, M¨unster, Germany, April 2011.
• 25th Automorphic forms workshop. Oregon state University, Corvallis, OR, March 2011.
• Winter meeting of the Canadian mathematical society. Vancouver, BC, December 2010.
• Midwest Number Theory Days. University of Wisconsin Madison, Madison, WI, November 2009.
• Midwest Number Theory Conference for Graduate Students VI. University of Wisconsin Madison, Madison, WI, November 2009.
• Conference on Higher degree forms. University of Florida, Gainesville, FL, May 2009.
• Encuentro en geometr´ıa y topolog´ıa de acciones de grupos. Universidad de los Andes, Bogot´a, Colombia, May 2009.
• Conference on Quadratic Forms, Sums of Squares, Theta Functions and Integral Lattices. University of Florida, Gainesville, FL, March 2009.
• Arizona Winter School, Quadratic forms. Project with Manjul Bhargava. University of Arizona, Tucson, AZ, March 2009.
• Taller en teor´ıa de n´umeros. Universidad de los Andes, Bogot´a, Colombia, October 2008.
• Arizona Winter School, Special functions and Transcendence. Project with Paula Tretkoff. University of Arizona, Tucson, AZ, March 2009.
• Midwest Number Theory Days. University of Illinois at Chicago, Chicago, IL March 2008.
• Midwest Number Theory Conference for Graduate Students V University of Wisconsin Madison. Madison, WI, November 2007.
• Summer School in Iwasawa Theory, Fields Institute. Hamilton, ON, August 2007.
• Summer School Homogeneous Flows, Moduli Spaces and Arithmetic. Clay Mathematics Institute, Centro De ricerca Matematica Ennio De Giorgi,Pisa,Italy, June 2007.
• What is Algebraic Geometry? Institute for Mathematics and Its Applications University of Minnesota, Minneapolis MN, April 2007.
• Arizona Winter School, p-adic Geometry. University of Arizona, Tucson, AZ, March 2007.
• Midwest Number Theory Conference for Graduate Students IV University of Illinois, Urbana, Champaign, October 2006.
• Tercera Escuela Matematica de Am´erica Latina y el Caribe. Morelia, Mexico, September 2003.
• Geometrical and Topological Methods for Quantum Field Theory I. CIMPA Summer School, Villa de Leyva, Colombia, July 2003.
• Segunda Escuela Matem´atica de Am´erica Latina y el Caribe. Merida, Venezuela, September 2002.
• I Encuentro de Aritm´etica. Universidad pedag´ogica, Bogot´a, Colombia, June 2002.
• Coloquio de Matem´atica de la Sociedad Peruana de Matem´aticas IMCA. Lima, Peru, Summer 2000.
• Geometrical and Topological Methods for Quantum Field Theory II. CIMPA Summer School, Villa de Leyva, Colombia, July 1999.
