Transcript Sara Perna – Curriculum Vitae

Sara Perna
Curriculum Vitae
Università degli Studi di Roma “La Sapienza”
Dipartimento di Matematica “Guido Castelnuovo”
Piazzale Aldo Moro 5, 00185 Roma
B [email protected]
B [email protected]
Personal information
Date of Birth April 15th , 1989
Place of Birth Napoli, Italy
Present position
11/2013-now PhD student in Mathematics, University of Rome “La Sapienza”
Expected December 2016
Advisor: Riccardo Salvati Manni
Research interests
Siegel modular forms and theta functions
Moduli spaces of abelian varieties and compactifications
Computational Algebraic Geometry
Education
10/2013 Master degree in Mathematics, “On the Superstring measure”, University of
Rome “La Sapienza”, 110/110 cum laude.
07/2011 Bachelor degree in Mathematics, “Branched coverings of the Riemann sphere
and Hurwitz formula”, University of Rome “La Sapienza”, 110/110 cum laude.
Master thesis
Title On the Superstring measure
Description The problem of finding an explicit expression for the superstring measure arises
in supersymmetric theories in physics which are also related to supergeometry, in
particular to the notion of super Riemann surfaces. For low genus the superstring
measure can be expressed in terms of theta constants and a fundamental tool in
finding this expression is the representation theory of finite groups.
Publications
1
“On isomorphisms between Siegel modular threefolds”, Abhandlungen aus
dem Mathematischen Seminar der Universität Hamburg, 86(1), 55-68.
Abstract: The Satake compactification of the moduli space of principally polarized abelian
surfaces with a level two structure has a degree 8 endomorphism. This compactification
can be viewed as a Siegel modular threefold. The aim of this paper is to show that this
result can be extended to other modular threefolds. The possibility of a similar situation in
higher dimensions is discussed at the end of the paper.
Preprints
“Heat equation for theta functions and vector-valued modular forms”,
arXiv:1510.03384.
Abstract: We give a new method for constructing vector-valued modular forms from
singular scalar-valued ones. As an application we prove the identity between two remarkable
spaces of vector-valued modular forms which seem to be unrelated at a first look, since
they are constructed in two very different ways. If Vgrad is the vector space generated by
vector-valued modular forms constructed with gradients of odd theta functions and VΘ is
the one generated by vector-valued modular forms arising from second order theta constants
with our new construction, we will prove that Vgrad = VΘ . This result could also be proven
as a consequence of the “heat equation” for theta functions.
“Vector-valued modular forms and the Gauss map”, arXiv:1505.06370, joint
work with F. Dalla Piazza, A. Fiorentino, S. Grushevsky, R. Salvati Manni.
Abstract: We use the gradients of theta functions at odd two-torsion points — thought
of as vector-valued modular forms — to construct holomorphic differential forms on the
moduli space of principally polarized abelian varieties, and to characterize the locus of
decomposable abelian varieties in terms of the Gauss images of two-torsion points.
In preparation
“On the construction of the moduli stack of Kummer varieties”, joint work
with Mattia Galeotti.
Conferences and Workshops
Participant
05/2016 Macaulay2 Workshop 2016, University of Warwick link
02/2016 Conference Algebraic Geometry in Torino, Torino link
08/2015 Summer School 2015 of the IRTG “Moduli and Automorphic Forms” Recent advances in algebraic and arithmetic geometry, Siena link
06-07/2015 PRAGMATIC 2015 Moduli of Curves and Line Bundles, Catania
link
05-06/2015 Workshop Algebraic Varieties and their Moduli, Centro di Ricerca Matematica De
Giorgi, Pisa link
07/2014 Graduate Workshop on Moduli of Curves, Simons Center Stony Brook University
link
05/2014 Conference Moduli and Automorphic Forms: a Meeting for Young Women in Mathematics, Berlin link
04/2014 Conference An induction day to supergeometry, Roma Tre University, Roma
02/2014 Workshop Curves and Equations, Levico Terme link
link
2
Speaker
11/2015 Mathematics Ph.D. Seminars, University of Torino link
12/2014 Conference Algebraic Geometry and Representation Theory in Rome 2nd edition,
Roma Tre University, Roma link
Organizer
12/2015 Conference Algebraic Geometry and Representation Theory in Rome 3rd edition,
University of Rome “La Sapienza”, Roma link
Languages
Italian native
English fluent, written and spoken
Computer skills
Programming Macaulay2, Mathematica, C++ (with particular knowledge in GiNaC library).
languages
Operating Linux, Windows.
systems
Updated
October 2016
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