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Guillermo Mantilla-Soler

Contact:

  • gmantillas@unal.edu.co

  • guillermo.mantillasoler@aalto.fi

  • g.mantilla691@uniandes.edu.co

I am an associate Professor in the Department of Mathematics  at Universidad Nacional de Colombia, in Medellín, and an adjunct Professor,  part of the ANTA group, in the Department of Mathematics at Aalto University in Helsinki. Previously, I was an associate Professor at Universidad de los Andes and a  research Professor at Universidad Konrad Lorenz . I was a postdoctoral researcher in the CSAG group at EPFL and in the number theory group at UBC.  My primary research fields are algebraic number theory and arithmetic geometry.  


Research, preprints and publications: 

Most of these(old versions) can be found in the arXiv.

  • Dense generic well-rounded lattices.(With C. Hollanti and N. Miller). SIAM Journal on Applied Algebra and Geometry. Vol. 9, No. 1, pp. 154-185(2025).

  • The shape of cyclic number fields. (With W. Bolaños). Canadian Mathematical Bulletin. Vol 66, Issue 2, 599-609. (2023).

  • Density questions on arithmetic equivalence.  Proceedings of the American Mathematical society. Vol 151, Number 7, 2783-2794. (2023).

  • The integral trace form as a complete invariant for real Sn number fields. (With C.  Rivera). Documenta Mathematica. Vol 27, 1865-1889. (2022).

  • Bases of minimal vectors in tame lattices.  (With M.T. Damir). Acta Arithmetica. Vol. 205 no.3, pp 265-285. (2022) 

  • Theta series and number fields:  theorems and experiments.  (With A. Barquero-Sánchez and N.C. Ryan.) Ramanujan Journal. 56, 613–630. (2021) 

  •  The trace form over cyclic number fields. (With W. Bolaños). Canadian Journal of Mathematics.  Vol 73, Issue 4, 947-969. (2021)

  • The $(\alpha, \beta)$-ramification invariants of a number field.  Mathematica Slovaca,  Vol. 71, No. 1, (2021)

  • An introduction to oddly tame number fields. Journal de Théorie des Nombres de Bordeaux,  Tome 32 no. 3, pp. 711-717. (2020). 

  •  A proof of a conjecture on trace-zero forms and shapes of number fields. (With C.  Rivera). Research in Number Theory 6, 35 (2020). 

  • Unit groups of quotients of number fields. (With J. Caro-Reyes). Communications of the Korean Math. Soc. 35 No 2. 481-486. (2020)

  • On a question of Perlis and Stuart regarding arithmetic equivalence.  New York journal of Mathematics 25, 558-573. (2019)

  • On a characterization of path connected topological fields. (With X. Caicedo)Journal of Pure and Applied Algebra  223 no. 12  5279-5284. (2019)

  • An $\ell-p$ switch trick to obtain a new proof of a criterion for arithmetic equivalence.  (With T. Bogart) Research in Number Theory 5, 1, (2019).

  • The Spinor genus of the integral trace form. Transactions of the American Mathematical society 369,1547-1577.  (2017)

  • The shape of Z/lZ-number fields. (With M. Monsurrò) Ramanujan Journal 39, no. 3 451-463.  (2016)

  • On the arithmetic determination of the trace. Journal of Algebra 444, 272-283. (2015)

  • Weak Arithmetic equivalence. Canadian Mathematical Bulletin, 58, 115-127. (2015).

  • 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, no. 7, 1569-1580. (2012)

  • Power map permutations and symmetric differences in finite groups. (With M. Hablicsek) Journal of Algebra and its applications 10, no. 5, 947-959.   (2011)

  • Integral trace forms associated to cubic extensions. Algebra and Number theory 4, no. 6, 681-699.  (2010)

  • The genus of the integral trace.  Useful reference to some of my papers.

  • Mordell-Weil ranks in towers of modular Jacobians. Ph.D thesis.

  • Automorfismos Polinomiales y la Conjetura de Keller. Sponsored by research fund of the Faculty of Sciences, Universidad de Los Andes. (2005)

Teaching:

     2025-I

  • Álgebra lineal 

  • Teoría algebraica de números


CV

News:  

Chaire Jean-Morlet - Conférence-Statistiques arithmétiques.

In May 2023 I'll be a plenary speaker on conference arithmetic statistics.  Click here for the poster.

Click here to find the slides of my talk in the NY # Theory seminar on March 2021.

Palmetto Number Theory series(PANTS)

In September(19-20) 2020  I'll be a plenary speaker in PANTS.

Number Theory in the Americas(A BIRS-CMO Workshop).

In August 2019 I was  part of research workshop in number theory. I'll be leading a research group working on applications of modular forms to totally real number fields.

Círculos Matemáticos. (Inscríbase acá)

Empezando en Marzo del 2019 varias Universidades locales se unen en un proyecto de participación en exploración de las Matemáticas. Los círculos están dirigidos a  estudiantes de Colegio de últimos años y serán liderados por investigadores y expertos en Matemáticas.  Para ver las actividades de los círculos bajo mi supervisión dar click acá.

Escuela en teoría de números(Teoría de Iwasawa).

In August 2018 Otmar Venjakob and I organized an instructional school  in Iwasawa theory.

Links:

  • NFT John Jones' tables of number fields.

  • arXiv arXiv, Number theory.

  • AGC Conferences in Arithmetic geometry.

  • NTC Conferences in Number theory. 

  • MSN MathSciNet.

  • SCM Sociedad Colombiana de Matemáticas.

  • AMS American mathematical society.


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