### Members of the Lie unit

- Website: Link

## Rafael Mrđen

#### Teaching assistant

**Position:**

- Teaching assistant at the Faculty of Civil Engineering, University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Representations of reductive groups, Dirac operators in representation theory
- Penrose transform, BGG-resolutions, D-modules

**Awards:**

- Award for outstanding achievement during the study from Dean of Department of Mathematics, and from Faculty council of Faculty of Science and Mathematics, University of Zagreb, 2011.

**Bio:**

Rafael Mrđen received a Master degree in Mathematics, from the Department of Mathematics, Faculty of Science and Mathematics, University of Zagreb, in 2011. His master thesis “Sheaf Cohomology” was under the supervision of prof.dr.sc Pavle Pandžić and doc.dr.sc. Zoran Škoda. He enrolled on the PhD Program at Department of Mathematics, University of Zagreb, received highest grades in all courses and exams, and gave numerous talks at the Seminar for Representation Theory. He is currently working on his thesis, which includes construction of the BGG-resolutions in a singular infinitesimal character, using the Penrose transform. He has been working as a teaching assistant at the Faculty of Civil Engineering since 2012, and has also worked at the Faculty of Science and Mathematics, and at the Faculty of Electrical Engineering and Computing, University of Zagreb.

## Matija Kazalicki

## Filip Najman

#### Associate Professor

**Position:**

- Associate Professor of Mathematics at the Faculty of Science University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Elliptic curves: Torsion over number fields, isogenies, Galois representations, modular curves

**Awards:**

- Annual Croatian State Award for Science for Young Researchers in 2010

**Five selected publications:**

- J. Bosman, P. Bruin, A. Dujella, F. Najman,
*Ranks of elliptic curves with prescribed torsion over number fields*, Int. Math. Res. Not. IMRN 2014 (2014), 2885-2923. - F. Luca, F. Najman,
*On the largest prime factor of x^2-1*, Math. Comp.**80 (**2011), 429-435. - S. Kamienny, F. Najman,
*Torsion groups of elliptic curves over quadratic fields*, Acta. Arith.**152**(2012), 291-305. - P. Bruin, F. Najman,
*A criterion to rule out torsion groups for elliptic curves over number fields*, Research in Number Theory**2** - F. Najman,
*Torsion of elliptic curves over cubic fields*, J. Number Theory,**132**

**The most important grants (as PI)**

- Fulbright Visiting Scholar with the project
*Arithmetic of Q-curves*, MIT, Cambridge, SAD,

**Bio:**

Filip obtained a MSc degree in mathematics from the University of Zagreb in 2007. and defended his PhD thesis at the same university in 2010 with the subject “*Compact representation of quadratic integers and integer points on elliptic curves*” under the supervision of prof. Andrej Dujella. From 2007. godine he has been employed as a research and teaching assistant at the Department of Mathematics of the Faculty of Science, from 2011. as an assistant professor, and from 2016. as an associate professor. His field of interest are number theory and arithmetic geometry, and elliptic curves in particular. He has published 22 papers, and 2 more have been accepted for publication.

He was on short research vistis in Graz, Debrecen, Strasbourg, Zurich, University of Warwick, University of Connecticut and University of Georgia. He recieved the *Postdoc* award from the Croatian Science Foundation for a stay in 2010/2011. at Universiteit Leiden in the Netherlands. As a winner of the Fulbright Visiting Scholar award for the year 2014/2015, through which he visited MIT, Cambridge, MA, SAD. He has taught 13 different courses at the undergraduate and graduate level, among which is the course Elliptic curves in cryptography, which he introduced jointly wiht prof. Andrej Dujella. He introduced and taught 2 courses at the doctoral school at the Department of Mathematics: Elliptic curves over number fields in the year 2012/2013 and Arithmetic Geometry in the year 2015/2016. He has been the mentor to 6 diploma theses, and was the co-mentor for the PhD thesis of Miljen Mikić. Since 2012. he has been the head of the graduate study program Theoretical mathematics.