Alessandro Lehmann

About me

Starting from October, I'll be an FWO postdoctoral fellow at the University of Antwerp. Previously I got my PhD at University of Antwerp and SISSA, under the supervision of Wendy Lowen and Nicolò Sibilla. Earlier I got my Master's in Sapienza University in Rome, where I did my thesis under Marco Manetti. Here is my CV.

Contact

• Alessandro Lehmann (he/him)
• University of Antwerp, Department of Mathematics
  Middelheimlaan 1, 2020
  Antwerp, Belgium
  alessandro.lehmann at uantwerpen dot be

Research

My main research area is (homological) algebra, with connections to deformation theory and noncommutative algebraic geometry.

More specifically, I am currently working on developing a deformation theory for (enhanced) triangulated categories. Here is a poster that explains my recent research in more detail.

Writing

A. Lehmann, W. Lowen, Hochschild cohomology and extensions of triangulated categories. Preprint.

A. Lehmann, Hochschild cohomology parametrizes curved Morita deformations. To appear in Proceedings of the AMS.

A. Lehmann, W. Lowen, Filtered derived categories of curved deformations. Preprint.

Miscellanea

Random writing

My master's thesis on enhancements of triangulated categories. I hope it can be useful as a reference for the basics or as a light introduction to some of the less elementary aspects of dg-categories. There are surely many imprecisions, ramblings and typos.

People

My research group in Antwerp: Violeta Borges Marques, Lander Hermans, Arne Mertens, Julie Symons, ...

Fish

The fish in the background is a betta splendens.

2024-2025

Algebraic Topology

I am teaching assistant for the course Algebraic Topology at the University of Antwerp, taught by Arne Mertens. Link

2023-2024

Hilbert and Fourier

I was teaching assistant for the course Hilbert spaces and Fourier series at the University of Antwerp, taught by Wim Vanroose. Link

2022-2023

Algebraic Topology

I was teaching assistant for the course Algebraic Topology at the University of Antwerp, taught by Jens Hemelaer. Link

2020-2021

Calcolo I

I was teaching assistant for the course Calculus I at Sapienza University, taught by Luigi Orsina.

Algebraic Topology

Session 1

Session 2

Homework 1

Session 3

Session 4

Homework 2

Session 5

Session 6

Session 7

Homework 3

Session 8

Session 9

Session 10

Solutions for session 10

Homework 4

Session 11

Session 12

Computation of singular homology of spheres via the Mayer-Vietoris sequence

Session 13

Session 14

Algebraic Topology

Here are some exercise sessions that I prepared for the course.

Session 1
Session 2
Session 3
Session 4
Session 5
Session 6
Session 7
Session 8
Session 9
Session 10

Hilbert and Fourier

Here are some exercise sessions that I prepared for the course.

Session 2
Session 3
Sessions 4 and 5

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';