[Dottorcomp] Invitation to MATHEMATICS Colloquium of MILANO | 28/05/2026 | University of Milano-Bicocca

[Michele D'Aquino]

*Thursday May 28, 2026* at *16.30* in Room U4-01 (first floor underground)
in the U4 building
<https://www.google.it/maps/place/45%C2%B030'50.8%22N+9%C2%B012'39.1%22E/@45.5141215,9.2103034,19z/data=!3m1!4b1!4m4!3m3!8m2!3d45.5141215!4d9.2108506>
of the University of Milano-Bicocca, located in Milano, Piazza della
Scienza 4


*CLAIRE VOISIN*
*IMJ-PRG Paris*



will present the first colloquium of the second cycle entitled



*Points and Zero-cycles of Algebraic Varieties*


*ABSTRACT*: An algebraic variety *X* is defined by polynomial equations in
an ambient space. The defining equations have coefficients in a field *K*.
When *K* is not algebraically closed, there might be no points of *X* defined
over *K*, but there are always points defined over finite extensions of *K*,
if *X* is non-empty. The study of these points is of interest both for
geometry and arithmetic. I will introduce the Chow group of zero-cycles of
*X*, which is built on these points and gives a partial way of computing
them, and its universal Chow group. The Chow group CH0(*X*) of zero-cycles
on*X* contains very important information. If the field *K* is the field of
complex numbers, one knows that it is related to holomorphic forms on
*X* (Mumford).
Over non-algebraically closed fields, the universal Chow group of
zero-cycles is related to rationality properties of *X*. I will discuss the
notion of Mumford finite vs. infinite dimensionality of CH0 and, on the
arithmetic side, the recently developed notion of boundedness vs.
unboundedness of CH0. I will also present related boundedness vs.
unboundedness statements about points on Fano hypersurfaces.



*RECEPTION:* Following the colloquium, there will be a reception in the U4
building (same floor of the lecture).



*ABOUT THE SPEAKER:* Claire Voisin is a French mathematician known for her
work in algebraic geometry. She is a member of the French Academy of
Sciences and held the chair of algebraic geometry at the Collège de France
from 2015 to 2020. She is noted for her work in algebraic geometry
particularly as it pertains to variations of Hodge structures and mirror
symmetry.

Among other prizes, Voisin won the European Mathematical Society Prize in
1992 and the Servant Prize awarded by the Academy of Sciences in 1996. She
received the Sophie Germain Prize in 2003 and the Clay Research Award in
2008 for her disproof of the Kodaira conjecture on deformations of compact
Kähler manifolds. She was an invited speaker at the 1994 International
Congress of Mathematicians in Zürich in the section 'Algebraic Geometry',
and a plenary speaker at the 2010 International Congress of Mathematicians
in Hyderabad.




*ORGANIZATION:*

Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano

Dipartimento di Matematica, Politecnico di Milano

Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca

Dipartimento di Scienze delle Decisioni, Università Bocconi Milano



In collaboration with: SEMINARIO MATEMATICO E FISICO DI MILANO



*DETAILS & CONTACTS:* visit the website of the MCM at https://www.mathcm.it or
write to one of the organizers:

fabrizio.andreatta a unimi.it

giovanni.catino a polimi.it

fabio.cipriani a polimi.it

gregorio.falqui a unimib.it

vincenzo.marra a unimi.it

kevin.payne a unimi.it

giuseppe.savare a unibocconi.it

thomas.weigel a unimib.it



On behalf of the organizers
--
Michele D'Aquino

Università degli Studi di Milano-Bicocca
Dipartimento di Matematica e Applicazioni
Via Roberto Cozzi, 55 - 20125 Milano