## Didactics

Teaching, mentoring and supervising are a relevant part of my academic activity. I have taught in several languages (English, Swedish, French and Italian) at University of Catania (2008-2009), at Stockholm University (2009-2014), at University of Fribourg (2014-2016), at Northeastern University (2016-2018), and at KTH (since 2019).

My

**teaching**portfolio has a large spectrum of courses at any academic level. I have also experience in developing courses (e.g. Extraseminars course at Stockholm University and Math Club at Northeastern University).

I have also

**supervised**more than 15 students for bachelor and master thesis. Many of them cover now doctoral or academic positions.

Below there is my teaching portfolio, department by department, or click here, The latest pdf version (Aug 2019) is available at this link.

#### List of courses I have taught:

At KTH: At Northeastern University:- Mathematics Capstone course - Undergraduate research - Math 4020 (Bachelor level);
- Introduction to mathematical reasoning - MATH1365 (Bachelor level);
- Jr/Sr Honors Project - MATH4970 (Bachelor level);
- Math Club (Bachelor and Master level);
- Experiential Ed Directed Study - MATH4996 (Master level);

- Algebra and Geometry II (Bachelor level);
- Algebra and Geometry I (Bachelor level);
- Background in matroid theory and commutative algebra (PhD/Master Minicourse);
- Introduction to toric varieties (PhD/Master Minicourse);
- Resolution of Singularities (PhD/Master Minicourse);
- The cohomology of complete smooth toric varieties using shellability (PhD Minicourse);
- Combinatorial methods in topology (Master Course);
- Méthodes mathématiques de l'informatique (Bachelor/Master course).

- Extraseminars (Bachelor level);
- Seminarisgruppen for Matematik I (Bachelor level);
- Räkneövning for Matematik I (Bachelor level);
- Handledning for Matematik I (Bachelor level);
- Handledning for Matematik D (Bachelor level);
- Optimization (Master Course).

- Geometry (Bachelor level).

#### My students:

- Alessio Borzì (Master, SSC): Matroids over a Domain; From Oct 2019, PhD student at Warkick;
- Jai ASLAM (Bachelor, NU): Group actions on Knots; Form Aug 2018 PhD student at NC State;
- Jean HARERIMANA (Master, NUR): Some mathematical models for population growth and Crowd motion;
- Victor LISINSKI (Extraseminar student, SU): Currently PhD student at University of Oxford;
- Alexis MANISHIMWE (Master, NUR): Hausdorff's measure and the Isoperimetric problem; now Assistant Lecturer at UTAB;
- Janvier NDAHIMANA RUKUNDO (Master, NUR): Genetic Algorithm and their applications;
- Niklas HEDBERG (Bachelor, SU): Numerical solutions of an ODE-system.

- Walker Miller-Breetz, together with Rahul Singh;
- Benjamin Bonenfant, together with Reuven Hodges;
- Zheying Yu, together with Celine Bonandrini;
- Kevin Su, together with Jonier Antunes; PhD student at UC Riverside, from Sept 2019;
- Christina Nguyen, together with Whitney Drazen;
- Noah Lichtblau, together with Mikhail Mironov;
- Felipe Castellano-Macias, together with Alex Sorokin; paper on ArXiv;
- Alon Duvall, together with Brian Hepler; PhD stutent at UC-San Diego;
- Timothy Jackman, together with Whitney Drazen; PhD student at Boston University;

#### Relevant Teaching Experience

**Extraseminars**

One interesting part of my teaching experience is the

*Extraseminars*course, an experimental

*Math Circle*style course started in October 2010 (supported by Boris Shapiro) and continued until 2014. I organized

*student-oriented*supplementary lectures for the most interested students of the first academic year of the science program of Stockholm University.

*The experience was successful.*I selected attractive mathematical topics following the taste of the students. For instance, I introduced projective geometry and let the students play with curves and surfaces. A good part of my job was mentoring these

*excellent*students in their first steps in Topology, Algebra and basic Algebraic Geometry. This experience has let me start mentoring and supervising students since the beginning of my academic career and I have always enjoyed that.

**Math Department consultant**

From autumn of 2016, I am

*Math Department consultant*of Mathematics Capstone course - Math 4020 Undergraduate research. In this course the students choose a topic, develop a proposal, write up and present a project of from 10 to 20 pages, involving some original thought. A large part of the course is practice in presenting the topic, and related mathematics. Students have used Math 4020 to get a feel for what research is like, and to help make a decision about whether to continue on to graduate school. Some have pursued further research, such as a summer Research Experiences for Undergraduates (REU).

**Math Club**

In September 2017, I was appointed as

*Faculty Advisor*and main organizer of the Math Club.

*The Northeastern Math Club*is a place where students interested in mathematics can get together and further explore mathematics outside of a classroom setting. We have weekly meetings which consist of a mix of both open discussions and talks given by professors, graduate students, and also some undergraduates.}

I was appointed as Faculty Advisor to shape this Club as

*Mathematical Lab*, a place where undergraduate students could meet different type of math and interact with the faculty of the math department.

#### Full Teaching Portfolio

My teaching is subdivided by the universities I have worked in.#### Teaching at KTH

**Spring 2020:**

__Lecturer__of Diskret matematik (7.5p) - SF1610 (Bachelor level);

**Spring 2019:**

__Lecturer__of Diskret matematik (7.5p) - SF1610 (Bachelor level);

__Advisor__of Alessio Borzi (Master level) for his diploma thesis;

#### Teaching at Northeastern University

**Autumn 2018:**

__Advisor__of Zheying Yu, Experiential Ed Directed Study - MATH4996 (Master level);

__Lecturer__of Introduction to mathematical reasoning - MATH1365 10197 (Bachelor level);

Classes are every Monday, Wednesday and Thursday at 13:35.

**Spring 2018:**

__Advisor__of Jai Aslam, Jr/Sr Honors ProjectJr/Sr Honors Project - MATH4970 36155 (Bachelor level);

**Autumn 2017:**

__Faculty Advisor__for the Math Club.

**Spring 2017:**

__Advisor__of Jai Aslam, Jr/Sr Honors Project - MATH4970 38489 (Bachelor level);

**Autumn 2016:**

__Math Department consultant__of Mathematics Capstone course - Undergraduate research - Math 4020 (Bachelor level).

__Lecturer__of Introduction to mathematical reasoning - MATH1365 10276(Bachelor level);

Classes are every Monday, Wednesday and Thursday at 13:35.

#### Teaching at University of Fribourg

My position does not involve teaching, but I am anyway covering some lecturer and teaching assistant duties.**Spring 2016:**

__Teaching assistant__for the course: Algebra and Geometry II;

The exercise sessions are every Tuesday at 15:15 to 17:00.

__Lecturer__of the minicourse: "Lessons on background in matroid theory and commutative algebra", May.

__Teaching assistant__for the course: Algebra and Geometry II;

The exercise sessions are every Tuesday at 15:15 to 17:00.

**Autumn 2015:**

__Advisor__of Jean Harerimana, thesis presentation in July 2016.

__Teaching assistant__for the course: Algebra and Geometry I;

The exercise sessions are every Tuesday at 15:15 to 17:00.

**Spring 2015:**

__Lecturer__of the minicourse: "The cohomology of complete smooth toric varieties using shellability", May.

__Lecturer__of the minicourse: "Resolution of Singularities", April.

__Lecturer__of the minicourse: "Introduction to toric varieties", March.

__Teaching assistant__for the course: Combinatorial methods in topology;

The exercise sessions are every Thurday at 13:15 to 14:00.

**Autumn 2014:**

__Teaching assistant__for the course: Méthodes mathématiques de l'informatique;

The exercise sessions are every Thurday at 10:15 to 12:00.

#### Teaching at Stockholm University (during my Ph.D).

In Sweden the PhD grant is normally for**4**years. If you decide to teach during your doctoral studies, then you get one year extension. In this case your time will be split as follows:

**80%**for the research and

**20%**for teaching.

**20%**of your time corresponds to

**300**hours of teaching every academic year.

I know what you are thinking: "

**300 hours of teaching is a lot!!**". You are right!!

Below are my teaching duties at Stockholm University:

Advisor Duty:

- Bachelor Advisor of NIKLAS HEDBERG. The thesis study the solutions of an ODE-system
- Master Advisor of JANVIER NDAHIMANA RUKUNDO. The thesis is about Genetic Algorithm and their applications.
- Master Advisor of MANISHIMWE ALEXIS. He study the Hausdorff's mesure and the Soap Bubbles conjecture.

Academic Year 2012-2013:

- Seminarisgruppen for Matematik I (Bachelor Course) [24 seminars, semester January-May 2013]
- Extraseminars (Bachelor Course) [semester January-May 2013, every week].

Academic Year 2011-2012:

- Seminarisgruppen for Matematik I (Bachelor Course) [12 seminars, semester August-December 2011]
- Extraseminars (Bachelor Course) [One year of seminars: 2011-12 every week]
- Extraseminars (Bachelor Course) [One year of seminars: 2012 every week]
- Seminarisgruppen for Matematik I (Bachelor Course) [12 seminars, semester January-May 2012]
- Räkneövning for Matematik I (Bachelor Course) [12 seminars, semester January-May 2012]
- Handledning for Matematik I (Bachelor Course) [12 times, semester January-May 2012]

Academic Year 2010-2011:

- Handledning for Matematik I (Bachelor Course)[24 times, semester January-May]
- Handledning for Matematik D (Bachelor Course)[12 times, semester January-May]
- Optimization (Master Course) [3 classes, semester January-May]
- Extraseminars (Bachelor Course) [5 classes, semester January-May]

#### Teaching at University of Catania (before my Ph.D).

Academic Year 2008-2009:__Teaching assistant__for the course*Geometria III*