#### WiSe 2016/17

##### Talk : Introduction to root systems in Lie algebras

The talks I will give are to be held in Klaus Altmann's seminar on 13.02.017 and 20.02.17, starting at 14:15. See webpage for more information.

##### Toric Varieties Seminar

Klaus Altmann's weekly seminar.

Mo 14:15-15:45, Arnimallee 3, Raum 119

See webpage for more information or potential modifications to the schedule.

#### Curriculum Vitae

Available here.

#### Publications

No papers available yet.

#### WiSe 16/17

No courses taught this semester.

The following is my personal database of moderately to completely cleaned up sets of notes. If you wish to comment/contribute/notice errors, feel free to do so via e-mail.

#### Representation Theory of Finite Groups

Version 09.01.2017 available here.

This is my personal introduction to representation theory. Currently, the only completed section is the one concerning the standard properties of representations and characters over $\mathbb C$. I plan on adding a second chapter over arbitrary fields and another chapter dedicated to the fascinating theory of representations of the permutation groups $S_n$ somewhere in the future.

#### Algebraic Groups and Lie Algebras

Version 09.01.2017 available here. These notes are not complete.

This will become my personal introduction to algebraic groups. Since they are closely related to their Lie algebras which is the tangent space at the identity, I began by writing an extensive section concerning Lie algebras with a focus in characteristic zero since I am interested in the reductive case. The notes will be further developed in the near future.

#### Introduction to Representation Theory

BMS Friday "What is...?" SeminarOctober 16

^{th}2015

A "What is...?" seminar is a ~20-25-minutes talk that answers a concise mathematical question in a manner accessible to students and mathematicians not familiar with the field. Get to know the many different parts of mathematics in a relaxed and open environment. We offer you the opportunity to meet other graduate students from various fields while enhancing your general knowledge of mathematics. Our speakers are welcome to experiment in their talks and enjoy the friendly feedback from the audience.

This "What is...?" seminar is meant to be a rough introduction to representation theory to be able to follow Geordie Williamson's talk. I sketch the basic concepts : definition of a representation, Maschke's theorem, Schur's Lemma and character theory. Since Geordie will mention modular representation theory I will give an example in characteristic p, where Maschke's theorem fails.

### Patrick Da Silva

Freie Universität Berlin

Fachbereich Mathematik und Informatik

Mathematisches Institut

Arnimallee 3, Büro 113

14195 Berlin

E-mail address: patrick1dasilva@gmail.com

StackExchange profile: Patrick Da Silva

Welcome to my academic homepage. I am currently a Phase II PhD student at the Berlin Mathematical School (BMS) under the doctoral supervision of Prof. Dr. Klaus Altmann and working on toric varieties.

My mathematical interests are mainly focused on algebraic geometry, but I am also interested in related/unrelated fields such as geometric invariant theory, representation theory, algebraic and analytic number theory, differential geometry, and "on the week-ends", probability theory and functional analysis.