Transcript A kind of CV - SISSA People Personal Home Pages
Fosco Loregian
“Never be misled by others.”
(last modified January 29, 2015)
Current base.
Oct 2012–?
PhD student , sissa , Trieste.
Tried to conquer the world, still failed. While I wait, I do some Category Theory in a hostile land.
What I want to do.
Category Theory applied to Algebra, Geometry and Physics, higher Category Theory, enriched Category Theory, monoidal categories, Topos Theory applied to Geometry, Logic, Homotopy Theory and Physics, Homological Algebra and Algebraic Topology, Homotopical Algebra, Abstract Algebra, higher dimensional Algebra, plot theory , Computational Homology, Haskell.
What I wrote.
in preparation in preparation in preparation Jan 2015 Homotopy coends in dg-categories , j/w F. Genovese (unipv) .
Récollements in stable ∞ -categories .
Stability conditions in stable ∞ -categories , j/w D. Fiorenza .
Hearts and Postnikov towers in stable ∞ -categories , with D. Fiorenza , arXiv 1501.04658
.
We exploit the equivalence between
t
-structures and normal torsion theories on stable ∞ -categories to unify two apparently separated constructions in the theory of triangu lated categories: the characterization of bounded t-structures in terms of their hearts and semiorthogonal decompositions on triangulated categories.
Jan 2015 This is the co/end, my only co/friend , arXiv 1501.02503
.
Aug 2014 A short note about co/end calculus, with unifying examples from Category Theory and Algebraic Topology.
t
-structures are normal torsion theories , with D. Fiorenza , arXiv 1408.7003
.
We characterize
t
-structures in stable ∞ -categories as suitable ization systems . More precisely we show that a
t
-structure t quasicategorical factor on a stable ∞ -category
C
is equivalent to a normal torsion theory F on
C
, i.e. to a factorization system F = ( E
,
M ) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.
H (+39) 347 350 8234 • B Via Bonomea, 265, 34136 Trieste – ITALY T (+39) 040 3787 860 • [email protected] • Í u (+39) 040 3787 528 http://people.sissa.it/ floregi/
2010–2012 2008–2010
Where I studied.
MSc.
, Università degli studi di Padova , Padua, Italy.
Master degree in Mathematics ( Laurea specialistica in Matematica ) BSc.
, Università degli studi di Padova , Padua, Italy.
Degree in Mathematics ( Laurea triennale in Matematica )
Doctoral thesis.
title (?) advisor Stability conditions in stable ∞ -categories Domenico Fiorenza, Università degli Studi di Roma “La Sapienza”, Italy description We are translating the theory of Bridgeland’s stability conditions on triangulated categories on the far more expressive and natural setting of stable ∞ -categories (quasicategorical model of Joyal-Lurie).
Masters thesis.
title advisor Orlov’s reconstruction theorem F. Bottacin, Università degli studi di Padova, Italy description As a consequence of the reconstruction theory paradigm, lots of algebraic properties of the derived category of a sufficiently nice space
X
reflect into geometric properties of the space itself, insofar you are often able to rebuild the whole
X
from scratch.
Nerd skills.
“Expert” A Mathematica, L TEX, TikZ Less expert Gnuplot, Matlab, Haskell
Stuff I taught.
Oct-Nov 2014 Homotopical Algebra , Università degli studi di Pavia , Italy, teacher (held in Italian).
Jan-Jun 2014 A series of lectures serving as an introduction to the language of Homotopical Algebra; starting from a a series of visually easy topological examples, it’s rather immediate to grasp the meaning of fibrations and cofibrations in abstract terms. A subsequent series of lectures (taking place during 2015) will adopt the language of Homotopical Algebra to familiarize the audience with the basics of Higher Category Theory.
Kan Extension Seminar , supervised by E. Riehl & other 11 disciples , Italy, Usa, Australia, UK, France. . . .
A graduate Category Theory reading course.
published on the
n
-Category Café.
More info here and on the posts we H (+39) 347 350 8234 • B Via Bonomea, 265, 34136 Trieste – ITALY T (+39) 040 3787 860 • [email protected] • Í u (+39) 040 3787 528 http://people.sissa.it/ floregi/
Jan 2014 Aug 2013 Jan 2011 Categorical Tools , Università degli studi di Padova , Italy, organizer and speaker (held in Italian).
A project (similar to the Jacobians mathematicians , see below) where I tried to propose a bit of categorical language to the “heathens” (pieces of enriched category theory, topos theory, groupoids in Algebraic Topology, categorical Homotopy Theory, weighted limits, coend-juggling, higher stuff. . . ).
CoG-GoC 2013 , sissa, Trieste , Italy, organizer and speaker (held in English/Italian).
Categories of Geometry, Geometry of Categories : The first experiment of a (would be) annual meeting I would like to organize with friends and colleagues. More info, a second manifesto and a detailed timetable here .
The Jacobian Mathematicians , Università degli studi di Padova , Italy, orga nizer and speaker (held in Italian).
A kind of “open window” towards the scientific attitude to knowledge. We did Maths instead of taking exams about Maths, also developing some interesting interconnection with culture and Philosophy.
Here you can read an (italian, never translated) manifesto.
During the whole experiment I delivered six talks (but three more people talked about { { { Game Theory, Fourier analysis, and analytical solutions to PDEs): { { Fibrations between spheres and Hopf theorem; The importance of being abstract , a gentle introduction to the categorical point of view to reality; low dimensional Topological Quantum Field Theories à la Atiyah; Chatting about complex geometry (symplectic, complex and Kahler manifolds); Connections and Fiber Bundles, with a glance to the geometry of Classical Field { Theory; A short lecure about Computational Homological Algebra , my first piece of (!) applied Mathematics.
Talks I gave.
Jan 2015 Jan 2015 May 2014 May 2014 Oct 2013 Aug 2013 Aug 2013 Categorical Resolutions, categorically , 1212.6170
, held in English, sissa - Trieste.
Lurification , following A. Kuznetsov’s arXiv A gentle intro to stable ∞ -categories , held in English, sissa Trieste.
How I learned to love the first quadrant , A gentle intro to the Serre spectral sequence , held in English, sissa - Trieste.
It’s turtles all the way down , Università degli studi di Bologna , A gentle introduction to Higher Category Theory.
Pursuing “ Pursuing stacks ” , Grothendieck homotopy theory in a nutshell , following Maltsiniotis .
Fourier-Mukai type transforms, categorically , inside CoG-Goc2013 .
This is the coend, my only cofriend , inside CoG-Goc2013 , 3 lectures about coend calculus.
H (+39) 347 350 8234 • B Via Bonomea, 265, 34136 Trieste – ITALY T (+39) 040 3787 860 • [email protected] • Í u (+39) 040 3787 528 http://people.sissa.it/ floregi/
Jun 2013 Apr 2013 Mar 2013 Dec 2012 The Algebra and Geometry of Categorical Groups , following TAC 16, 20 and Baez , held in English, sissa - Trieste.
Homotopical interpretation of stack theory , with a crash course on Topos theory , following Joyal and Tierney , held in English, sissa - Trieste.
Categorification on AQFT , following arXiv:1209.0124
, held in English, sissa Trieste.
Homotopical Algebra for C ∗ -algebras , following O. Uuye , held in English, sissa - Trieste.
H (+39) 347 350 8234 • B Via Bonomea, 265, 34136 Trieste – ITALY T (+39) 040 3787 860 • [email protected] • Í u (+39) 040 3787 528 http://people.sissa.it/ floregi/