## 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) and at Northeastern University (From 2016).

My

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

In my career I have been close

**mentor**of many undergraduate students (e.g. Victor Lisinski, accepted in Oxford in Sept 2017) and many PhDs (e.g. Simone Cecchini (University of Göttingen)).

I have also

**supervised**a large number of bachelor and master thesis.

Below is my portfolio, department by department, or click here. The latest pdf version (Aug 2018) is available here.

#### List of courses I have taught:

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:

- 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;
- 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;
- Christina Nguyen, together with Whitney Drazen;
- Noah Lichtblau, together with Mikhail Mironov;
- Felipe Castellano-Macias, together with Alex Sorokin;

#### 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 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*