Math

I am mostly interested in number theory and algebra. I studied number theory (automorphic forms) under the guidance of Professor Freydoon Shahidi as my PhD at Purdue, whereas in Prague it was rather algebra, mostly the theory of semirings. My Bachelor's and Master's theses are about them.

During Fall 2014 I'll be a postdoc at the Max Planck Institute in Bonn, then I'll continue for 2 years at the University of Göttingen.

Curriculum Vitae

Research Statement

Teaching Statement

Research

My work is on automorphic forms, a modern area of number theory. My PhD thesis problem is related to the Weyl's Law that gives the asymptotics for the number of automorphic forms in terms of their Laplacian eigenvalue. Using properties of functorial descent (and other things, for example the notion of depth of a local representation), I prove a similar upper bound on the number of self-dual cuspforms on GL_n(A_Q). I have also been working on the relation between local descent and depth and plan to work more on this and other related problems in the future.

A poster presentation on the Langlands program and my work (primarily for non-mathematicians) for the International Fulbright Science and Technology Conference in 2012 is here.

Theses

V. Kala: Density of Self-Dual Automorphic Representations of GL_n(A_Q), 2014, PhD thesis, advisor F. Shahidi

V. Kala: Simple semirings, 2009, Master's thesis (Mgr.), advisor T. Kepka

V. Kala: Simple semirings, 2007, graduation thesis (Bc.), advisor T. Kepka

V. Kala: Prvociselne vzorce (Prime-generating functions), 2004, high school graduation thesis, supervisor R. Kucera

Articles

Please email me if you are interested in copies or preprints of my theses and papers.

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J. Berg, A. Castillo, R. Grizzard, V. Kala, R. Moy, C. Wang: Congruences for Ramanujan's f and omega functions via generalized Borcherds products, Ramanujan Journal, accepted.

J. Jezek, V. Kala, T. Kepka: Finitely generated algebraic structures with various divisibility conditions, Forum Math. 24 (2012), pp. 379 - 397.

V. Kala, M. Korbelar: Congruence simple subsemirings of Q^+, Semigroup Forum 81 (2010), pp. 286 - 296.

A. Drapal, C. Hamalainen, V. Kala: Latin bitrades, dissections of equilateral triangles and abelian groups, J. Comb. Des. 18 (2010), pp. 1 - 24.

V. Kala, T. Kepka, P. Nemec: Norms on semirings I, Acta Univ. Carolin. Math. Phys. 51 (2010), pp. 29 - 48.

V. Kala, T. Kepka: Commutative parasemifields finitely generated as semirings, Acta Univ. Carolin. Math. Phys. 51 (2010), pp. 49 - 56.

V. Kala, T. Kepka, M. Korbelar: Notes on commutative parasemifields, Comment. Math. Univ. Carolin. 50 (2009), pp. 521 - 533.

V. Kala, A. D. Keedwell: Addendum to "The existence of Buchsteiner and conjugacy-closed quasigroups", Europ. J. Combin. 30 (2009), p. 1386.

V. Kala, T. Kepka, M. Korbelar, J. D. Phillips: Various subsemirings of the field Q of the rational numbers, Acta Univ. Carolin. Math. Phys. 50 (2009), pp. 29 - 59.

V. Kala, T. Kepka: A note on finitely generated ideal-simple commutative semirings, Comment. Math. Univ. Carolin. 49 (2008), pp. 1 - 9.

V. Flaska, A. Jancarik, V. Kala, T. Kepka: Trees in commutative nil-semigroups of index two, Acta Univ. Carolin Math. Phys. 48 (2007), pp. 81 - 101.

Student Colloquium

Teaching at Purdue

MA 223, Spring 2014 MWF 1.30, 2.30 in PHYS 338

MA 223, Spring 2013

Teaching at Charles University

Class Field Theory (two-week intensive course) - spring 2010/2011

Number Theory and RSA (lecture and recitation) - spring 2008/2009

Number Theory and RSA (recitation) - spring 2007/2008

Number Theory and RSA (recitation) - spring 2006/2007

Number Theory and RSA (recitation) - spring 2005/2006

Number Theory Proseminar - spring 2007/2008

Number Theory Proseminar - spring 2006/2007

Algebra Recitation - spring 2008/2009

Fundamentals of Algebra (recitation) - fall 2007/2008

Contact

My email adress is vita.kala, the server is gmail com.

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