guillermo mantilla-soler - Universidad de los Andes

GUILLERMO MANTILLA-SOLER
Department of Mathematics
Universidad de los Andes
Bogotá, Colombia.
+(571) 3394949 Ext 5220
[email protected]
matematicas.uniandes.edu.co/∼gmantilla
Employment
Universidad de los Andes
Assistant Professor
Bogotá, Colombia
2014-
École Fédérale Polytechnique de Lausanne
Postdoctoral research fellow
Mentor: Eva Bayer-Fluckiger
Lausanne, Switzerland
2012-2014
University of British Columbia
Postdoctoral research fellow
Mentor: Nike Vatsal
Vancouver, BC, Canada
2010-2012
Education
University of Wisconsin-Madison
Ph.D. in Mathematics.
M.A. in Mathematics
Madison, Wisconsin, USA
2010
2006
• Advisor Jordan S. Ellenberg
Universidad de los Andes
M.S. in Mathematics
B.S. in Mathematics
Bogotá, Colombia
2005
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 Adelic, Arithmetic and weak Arithmetic equivalences between number fields. In preparation
• A classification of locally path connected topological fields. In preparation.
• A characterization of arithmetic equivalence via Galois representations. Preprint
• The genus of the integral trace form. In preparation.
• The spinor genus of the integral trace form. Transactions of the American Mathematical Society DOI:
10.1090/tran/6723
• The shape of Z/`Z-number fields. With M. Monsurrò. Ramanujan Journal (2016) Vol 39, 3, 451-463.
• 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 1 modular 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 Márton 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 I/Group theory, Algebra II/Galois theory, Second course in linear algebra, Algebraic number theory,
Intro to Algebraic Geometry. 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). See http://matematicas.uniandes.edu.co/~gmantilla/Teaching/SEP.htm for 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, Bogotá,
Colombia, January 2001-May 2005.
• Lecturer, Calculus I,II, Linear Algebra and Discrete Math. Universidad de los Andes, Bogotá, Colombia,
January 2001-May 2005.
• Lecturer, Business Mathematics. Universidad del Rosario, Bogotá, Colombia, January 2004-May 2004.
• Instructor, Algebra Summer Course. Colegio San Carlos, Bogotá, Colombia, Summer 2001.
Students supervised.
Ongoing
• 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.
• Jose Miguel Cruz. Undergraduate, Universidad de los Andes.
• Yacir Ramirez. Master, Universidad de los Andes.
• Juan Esteban Rodriguez(co-advised with Jorge Plazas). Undergraduate, Universidad Javeriana, Bogotá.
Former students
• Luı́s Felipe Vargas, El teorema de Kronecker Webber. Undergraduate Thesis, Universidad de los Andes.
Spring 2016
• Approche algébrique du thórème de la progression arithmétique de Dirichlet by Gaüetan Gogniat. Third year
year project at EPFL co-supervised by Eva Bayer-Fluckiger. Spring 2014.
• An elementary proof of the fundamental theorem of algebra by Filip Fifka. Second year project at EPFL ,
co-supervised by Eva Bayer-Fluckiger. Spring 2014.
• Sur la transcendance de π et le thórème de Lindemann-Weierstrass by Philippe Atten. Fourth year project at
EPFL co-supervised by Eva Bayer-Fluckiger. Fall 2013.
• Les nombres p-adiques by Erwan kohler. Third year project at EPFL co-supervised by Eva Bayer-Fluckiger.
May 2013.
Talks
Research talks
• Invited speaker, Second Mathematical Congress of the Americas special session on Arithmetic Geometry and
Related Topics. Montreal, CA, July 2017.
• Invited speaker, Joint meeting special session on Analytic Number Theory and Arithmetic. Atlanta, GA,
January 2017.
• Invited speaker, CMS Winter meeting, Special Session on algebraic number theory. Montreal, Canada,
December 2015.
• Invited Speaker, 29th Journées Arithmétiques, Debrecen, Hungary, July 2015.
• Invited Speaker, Sextas Jornadas en Teorı́a de números, 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 Séminaire d’Algèbre et de Théorie des Nombres, EPFL, Switzerland, July 2014.
• Invited Speaker, Séminaire de Théorie des Nombres, Institute de Mathématiques 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 arithmétique , Laboratoire de mathématiques de Besançon, France,
December 2013.
• Invited Speaker, Algebra, geometry and number theory seminar, Universiteit Leiden, Netherlands, November
2013.
• Invited Speaker, Colloquium, Université de Neuchâtel, Switzerland, October 2013.
• Invited Speaker, Emory Algebra and Number Theory Seminar, Atlanta, GA, September 2013.
• Invited Speaker, Québec-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 Teorı́a de números, Seville, Spain, July 2013.
• Invited Speaker, 28th Journées Arithmétiques, Grenoble, France, July 2013.
• Invited Speaker, Seminario di Geometria Algebrica, Universitá Europea di Roma, Italy, June 2013.
• Invited Speaker, Séminaire de Théorie des Nombres Université Blaise Pascal, Clermont-Ferrand, France, May
2013.
• Invited Speaker, Universidad Sergio Arboleda, Bogotá, Colombia, February 2013..
• Invited Speaker, Seminario de Álgebra Universidad de Los Andes, Bogotá, Colombia, February 2013.
• Invited Speaker, Séminaire d’Algèbre et de Théorie des Nombres, Laboratoire de mathématiques de
Besançon, France, February 2013.
• Invited Speaker, Algebra and combinatorics seminar, Aalto University, Helsinki, Finland, December 2012.
• Speaker at Séminaire d’Algèbre et de Théorie des Nombres, EPFL, Switzerland, October 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 on p-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 introducción a las representaciones de Galois y a la teorı́a de Iwasawa. Universidad Industrial de
Santader, Bucaramanga, Colombia, 2016.
• Una introducción a la teorı́a algebraica de números y a equivalencia arimética. Universidad Javeriana,
Bogotá, Colombia, 2016.
• Una introducción a las representaciones de Galois y a la teorı́a de Iwasawa. Universidad de los Andes,
Bogotá, Colombia, 2015.
• El último teorema de Fermat. Main speaker for a two week workshop on FLT. Universidad de Antioquia,
Medellı́n, Colombia, 2015.
• Quadratic forms in number theory. CUSO Doctoral School, Les Diablerets, Switzerland, March 2014.
• El principio de Hasse, Taller en teorı́a de números. Universidad de los Andes, Bogotá, Colombia, October
2008.
Expository talks
• Formas cuadráticas racionales y el principio global vs local. Conferencista invitado a la tercera escuela de
Matemáticas, Universidad los Libertadores, Bogotá, 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.
• étale 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 geometrı́a y topologı́a de acciones de grupos. Universidad de los Andes,
Bogotá, 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 of Zp 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, Bogotá, Colombia, March 2005.
• El ı́ndice como Morfismo de Monoides definido sobre los Operadores de Fredholm. Universidad de los Andes,
Bogotá, 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, Bogotá, Colombia, June 2003.
• El problema de integracion de funciones elementales en Terminos finitos. Universidad de los Andes, Bogotá,
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 Matemáticas
• Organizer of the Algebraic number theory and related topics session at CLAM 2016. Universidad del Norte,
Barranquilla, Colombia, July 2016.
• Coordinador for Linear algebra, Universidad de los Andes. August 2016–
• Organizer of the Mathematics Colloquium, Universidad de los Andes. January 2015–January 2016
• Library coordinator of the Mathematics department, Universidad de los Andes. January 2015–January 2016
• 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
grading classificatory and final rounds of competitions.) Colombian Mathematical Olympiad, Bogotá,
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.
Conferences and Workshops attended
• ALTENCOA 7, Bucaramanga Colombia, Colombia, July 2016.
• Congreso Latinoamericano de Matemáticas, Barranquilla, Colombia, July 2016.
• Non Commutative Geommetry, Villa de Leyva, Colombia, June 2016.
• 29th Journées Arithmétiques, Debrecen, Hungary, July 2015.
• Sextas Jornadas en Teorı́a de números, Valladolid, Spain, July 2015.
• Counting arithmetic objects(Ranks of elliptic curves), Montreal, Canada, November 2014.
• Quintas Jornadas en Teorı́a de números, Seville, Spain, July 2013.
• 28th Journées Arithmétiques, Grenoble, France, July 2013.
• Seminario di Geometria Algebrica, Universitá 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, Münster, 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 geometrı́a y topologı́a de acciones de grupos. Universidad de los Andes, Bogotá, 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 teorı́a de números. Universidad de los Andes, Bogotá, Colombia, October 2008.
• Arizona Winter School, Special functions and Transcendence. Project with Paula Tretkoff. University of
Arizona, Tucson, AZ, March 2008.
• 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 América 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 Matemática de América Latina y el Caribe. Merida, Venezuela, September 2002.
• XIII Encuentro de Geometrı́a y sus Aplicaciones. Universidad pedagógica, Bogotá, Colombia, June 2002.
• I Encuentro de Aritmética. Universidad pedagógica, Bogotá, Colombia, June 2002.
• Coloquio de Matemática de la Sociedad Peruana de Matemáticas IMCA. Lima, Peru, Summer 2000.
• Geometrical and Topological Methods for Quantum Field Theory II. CIMPA Summer School, Villa de Leyva,
Colombia, July 1999.