Extended Curriculum - Institut Camille Jordan

Antonio Lerario
Institut Camille Jordan
Universit´e Claude Bernard Lyon 1
43 boulevard du 11 novembre 1918
69622 Villeurbanne cedex France
[email protected]
[email protected]
Born on April 7, 1984, in Desenzano Del Garda (BS), Italy
Position
Institute Camille Jordan, Lyon
ERC-CNRS Postdoc
Appointments
Purdue University
Visiting Assistant Professor
Education
S.I.S.S.A. - I.S.A.S.
PhD in Geometry
from January 2014
January 2012 - December 2013
2011
Thesis: Homology invariants of quadratic maps
Advisor Prof. A. A. Agrachev
I.U.S.S. Pavia
Diploma Scuola Universitaria Superiore
2009
(Additional Diploma in Mathematics awarded by the Institute for Advanced Studies of Pavia; the
admission is on a merit base)
Universit`
a Degli Studi di Trieste
Laurea Magistrale in Matematica
(Master’s Degree in Mathematics)
110/110 Cum Laude
2008
S.I.S.S.A. - I.S.A.S.
Diploma Percorso Formativo Comune
2008
(Additional Diploma in Mathematics awarded by the International School for Advanced Studies; it
is assigned on a merit base)
Universit`
a Degli Studi di Pavia
Laurea Triennale in Matematica
(Bachelor’s Degree in Mathematics)
110/110 Cum Laude
Fellowships and Academic Distinctions
IHP, Paris
Fellow for a trimester on subriemannian
Geometry
IHP, Paris
Research in pairs
(together with E. Lundberg)
2006
September-December 2014
June-July 2014
S.I.S.S.A. - I.S.A.S.
Phd Fellowship - Geometry curriculum
2008-2011
S.I.S.S.A. - I.S.A.S.
Borsa di studio Percorso Formativo Comune
2006-2008
(Fellowship assigned by the International School for Advanced Studies through a national competition; the confirmation of the fellowship is on a merit base)
I.U.S.S. Pavia
Borsa di studio Alunno Classe di Scienze
2002-2006
(Fellowship assigned by the Institute for Advanced Studies of Pavia through a national competition;
the confirmation of the fellowship is on a merit base)
Almo Collegio Borromeo Pavia
Merit alumn
2002-2006
(The position as a student of the College is assigned through a national competition; the confirmation
of the fellowship is on a merit base)
Mathematical Interests
Real Algebraic Geometry, Algebraic Topology, Random Geometry, Subriemannian Geometry.
Honors and Additional Distinctions
Invited speaker at the Mathematics Colloquium, University of Toronto, 2011.
Invited speaker at the Mathematics Colloquium, SISSA 2013
Invited speaker at FOCM’14 (Uruguay) in two different sessions: Real number complexity and Random matrices.
Teaching experience
Spring 2011, Purdue University, MA265 (Linear Algebra).
Fall 2012, Purdue University MA265 (Linear Algebra).
Spring 2013, Purdue University MA265 (Linear Algebra).
Fall 2013, Purdue University MA265 (Linear Algebra).
Papers
1) (with A. A. Agrachev) Systems of quadratic inequalities
Proceedings of the London Mathematical Society, 2012, 105 (3): 622-660, DOI: 10.112/plms/ds010
2) Convex pencils of real quadratic forms
Discrete and computational Geometry, 2012, DOI: 10.1007/s00454-012-9460-2
3) The total Betti number of the intersection of three real quadrics
Advances in Geometry, to appear
4) Random Matrices and the average topology of the intersection of two quadrics
Proceedings of the American Mathematical Society, to appear
5) Complexity of intersection of quadrics and topology of symmetric determinantal varieties
Journal of the European Mathematical Society, to appear
6) Plenty of Morse functions by perturbing with sums of squares
Proceedings Gokova Geometry and Topology, to appear
7) (with E. Lundberg) Statistics on Hilbert’s Sixteenth Problem
International Mathematics Research Notices, doi: 10.1093/imrn/rnu069
8) (with D. Barilari) Geometry of Maslov cycles
Geometric Control and Sub-Riemannian Geometry, Springer INdAM series, to appear
9) (with S.-Y. Lee and E. Lundberg) Remarks on Wilmshurst’s theorem
Indiana University Mathematics Journal, to appear
10) (with A. A. Agrachev and A. Gentile) Geodesics and horizontal-path spaces in Carnot groups
Geometry & Topology, to appear
11) (with J. Hauenstein, E. Lundberg and D. Mehta) Experiments on the zeros of harmonic polynomials
using certified counting
Experimental Mathematics, to appear
12) (with Y. V. Fyodorov and E. Lundberg) On the number of connected components of random hypersurfaces
Journal of Geometry and Physics, conditionally accepted
13) A real viewpoint on intersections of complex quadrics and their topology
arXiv:1106.1828
14) (with E. Lundberg) Gap probabilities and applications to geometry and random topology
submitted
15) Intrinsic volumes of sets of singular matrices and applications to real algebraic geometry
submitted
16) (with L. Rizzi) How many geodesics join two points on a contact sub-Riemannian manifold?
submitted
Invited talks and conferences
1) Mathematics Colloquium at the University of Toronto, January 2011, Systems of quadratic inequalities
2) McMaster University, Analysis seminar, January 2011, Topology of intersections of real quadrics
3) Courant Institute of Mathematical Sciences, Algebraic Geometry Seminar, February 2011, Systems
of quadratic inequalities
4) Conference in Real Algebraic Geometry, Rennes, June 2011, Systems of quadratic inequalities
5) Department of Mathematics, Rennes, November 2011, The total Betti number of the intersection of
three real quadrics
6) Geometric Control and Subriemannian geometry Conference, Cortona, June 2012, The topology of
a random intersection of real quadrics
7) SISSA, May 2012, Expected topology of random real algebraic varieties
8) AskoldFest, Moscow, June 2012, Complexity of intersection of real quadrics
9) Dipartimento di Matematica, Pavia, July 2012, Topology of intersections of real quadrics
10) Department of Mathematics, Rice Univeristy, Novemeber 2012, Real Determinantal curves and nets
of quadrics
11) Department of Mathematics, Texas A&M, November 2012, Complexity of intersections of real
quadrics and topology of symmetric determinantal varieties
12) Felix Klein seminar, Department of Mathematics, Notre Dame University, April 2013, Statistics on
Hilbert’s Sixteenth Problem
13) Courant Institute of Mathematical Sciences, Geometry seminar, May 2013, Complexity of intersections of real quadrics and topology of symmetric determinantal varieties
14) Mathematics colloquium, SISSA June 2013, Statistics on Hilbert’s Sixteenth problem
15) ZIF, Bielefeld, August 2013, Statistics on Hilbert’s Sixteenth problem
16) Department of Mathematics, Texas A&M, October 2013, Topology of loop spaces in Carnot groups
17) Institute for Advanced Studies, Princeton, October 2013, Gap probabilities and applications to geometry and random topology
18) Purdue University, Department of Mathematics, November 2013, A random intersection of quadrics
is on average connected
19) IHP, Paris, January 2014, Loop spaces in subRiemannian geometry
20) SISSA, February 2014, Counting nodal lines of random hypersurfaces
21) SISSA, February 2014, Intrinsic volumes of singular matrices
22) SISSA, March 2014, Random matrices and applications to geometry and random topology
´
23) S´eminaire de G´eom´etrie Tropicale, Ecole
Polytechnique, Paris, March 2014, A random intersection
of quadrics is on average connected
24) IRMA, Strasbourg, March 2014, Counting the number of components of random real hypersurfaces
25) Steklov Mathematical Institute, Moscow, April 2014, How many geodesics are there between two
close points on a subriemmanian manifold?
26) Institut Camill Jordan, Lyon, April 2014, Homology of intersection of real quadrics
27) Intitut Fourier, Grenoble, May 2014, Gap probabilities and applications to geometry and random
topology
28) Second Joint International Meeting IMU-AMS, Tel Aviv, June 2014, Topology of random intersection
of real quadrics
29) LSIS Toulon, June 2014, Enumerative geometry of geodesics on contact sub-riemannian manifolds
30) International conference on geometry and analysis on metric spaces, Baikal lake, August 2014,
Topology of nonholonomic loop spaces
31) Institut de math´ematiques de Jussieu, October 2014, Counting the number of components of random
real hypersurfaces
32) EPFL, Lausane, October 2014, Quantitative topology of nonholonomic loop spaces
33) Institut Camill Jordan, Lyon, November 2014, Quantitative topology of nonholonomic loop spaces
34) Institut de Math´ematiques de Bourgogne, November 2014, Nodal lines of random hypersurfaces
35) IHP, Paris, November 2014, Geodesics and horizontal loop spaces in Carnot groups
36) S´eminaire de Topologie, Institut de Math´ematiques de Jussieu - Paris Rive Gauche, November 2104,
Homology of intersections of real quadrics
37) S´eminaire de G´eom´etrie, Chamb´ery, November 2014, Complexity of intersections of real quadrics
and the topology of discriminant varieties
38) IHP, Paris, November 2014, Quantitative topology of nonholonomic loop spaces
Referee service
Journal of the European Mathematical Society
Arnold Mathematical Journal
Geometric Control and subriemannian geometry
Romanian Mathematical Journal
Siam Journal on Control and optimization
Ph.D. students
A. Gentile (Sissa, October 2014).
Languages
Italian: mother tongue
English: fluent
French: good knowledge
Personal Webpage
http://math.univ-lyon1.fr/∼lerario/homepage/Home.html
References
Andrei Agrachev (thesis advisor, Sissa,Trieste): [email protected]
Saugata Basu (Purdue University): [email protected]
Boris Dubrovin (Sissa, Trieste): [email protected]
Ilia Itenberg (Jussieu, Paris): [email protected]
Viatcheslav Kharlamov (IRMA, Strasbourg): [email protected]
Askold Khovanskii (University of Toronto): [email protected]
Peter Sarnak (IAS, Princeton): [email protected]