### Members of the Lie unit

## Prof. Pavle Pandžić

**Position:**

- Professor of Mathematics, Faculty of Science, University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Representation theory of real reductive Lie groups, Lie algebras and superalgebras
- Algebraic and holomorphic geometry, D-modules

**Awards:**

- Annual Croatian State Award for Science in 2012

**Five selected publications:**

- -S.Huang, P.Pandžić,
*Dirac cohomology, unitary representations and a proof of a**conjecture of Vogan*, J. Amer. Math. Soc. 15 (2002), 185-202.

- -S.Huang, P.Pandzic, G.Savin,
*New dual pair correspondences*, Duke Math. J. 82 (1996), 447-471.

- Pandžić,
*Zuckerman functors between equivariant derived categories*, Trans. Amer. Math. Soc. 359 (2007), 2191-2220. - -S.Huang, P.Pandžić, F.Zhu,
*Dirac cohomology, K-characters and branching laws*, Amer. J. Math. 135 (2013), no.5, 1253-1269. - Mehdi, P.Pandžić, D.Vogan,
*Translation principle for Dirac index*, to appear in Amer. J. Math.

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

- 2015- Leader of the Research unit for representation theory of Lie algebras, number theory, and associated structures of the Center of excellence for quantum and complex systems and representations of Lie algebras – QuantiXLie
- 2014- PI of the grant „Dirac operators in representation theory“ funded by the Croatian Science Foundation
- 2002-2013 PI of two grants funded by the Ministry of Science and Technology of the Republic of Croatia
- 2002-2013 PI of three bilateral Croatian-French grants.

**Bio:**

Pavle Pandžić graduated mathematics at the Department of Mathematics, Faculty of Science, University of Zagreb, in 1986. He obtained his Master degree at the same institution in 1989. From 1990 to 1995 he attended the graduate program at University of Utah, Salt Lake City, USA, where he obtained his Ph.D. degree in 1995. His advisor was D.Miličić. From 1995 to 1998 he was a C.L.E. Moore Instructor at Massachusetts Institute of Technology, Cambridge, USA. In 1998 he returned to University of Zagreb, where he has since held the positions of Research Assistant, Assistant Professor, Associate Professor and finally Full Professor since 2010. After returning to Zagreb, he held long-term visiting positions in Singapore, Japan, Hong Kong, USA, France and Germany. He is an author of 30 publications, and a scientific monograph „Dirac operators in representation theory“. He gave around 30 invited lectures at conferences, and around 30 lectures at seminars and colloquia at various places he was visiting. His subjects of interest are representations of real reductive groups, in particular (g,K)-modules and their homological algebra. His main results concern applications of Dirac operators to (g,K)-modules.

He received the Annual Croatian State Award for Science in 2012. He supervised one finished Ph.D. student, and currently he is supervising four Ph.D. students. He was the PI of several scientific grants. He held various administrative positions at the Department of Mathematics. He was the Editor in Chief of the scientific journal Glasnik matematički. He taught many courses in algebra, analysis and geometry.

- Website: Link

## Andrej Dujella

#### Academician, Professor

**Position:**

- Professor of Mathematics at the Faculty of Science University of Zagreb (Department of Physics)
- Full member of the Croatian Academy of Sciences and Arts

**Fields of interest:**

- Number theory: Diophantine equations and Diophantine approximations, elliptic curves, applications of number theory to cryptography

**Awards:**

- Croatian Mathematical Society Award for Scientific Achievements in Mathematics in 2000
- Award of the Croatian Academy of Sciences and Arts in 2004
- State annual award for science in 2006

**Five selected publications:**

- Dujella,
*There are only finitely many Diophantine quintuples*, J. Reine Angew. Math. 566 (2004), 183-214. - Bosman, P. Bruin, A. Dujella and F. Najman,
*Ranks of elliptic curves with prescribed torsion over number fields*, Int. Math. Res. Not. IMRN 2014 (11) (2014), 2885-2923. - Dujella and C. Fuchs,
*Complete solution of a problem of Diophantus and Euler*, J. London Math. Soc. 71 (2005), 33-52. - Bugeaud and A. Dujella,
*Root separation for reducible integer polynomials*, Acta Arith. 162 (2014), 393-403. - Dujella and A. Pethő,
*A generalization of a theorem of Baker and Davenport*, Quart. J. Math. Oxford Ser. (2), 49 (1998), 291-306.

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

- 2014-2018 Principal investigator of the project Diophantine
*m*-tuples, elliptic curves, Thue and index form equations, funded by the Croatian Science Foundation) - 2007-2013 Principal investigator of the project Diophantine Equations and Elliptic Curves, funded by the Croatian Ministry of Science, Education and Sport
- 2004-2011 Principal investigator (with Robert Tichy) of four bilateral Croatian-Austrian projects
- 2005-2014 Principal investigator (with Yann Bugeaud) of three bilateral Croatian-French projects
- 2005-2011 Principal investigator (with Attila Pethő) of two bilateral Croatian-Hungarian projects

**Bio:**

Andrej Dujella received a PhD in mathematics from the University of Zagreb in 1996. He has been promoted to the rank of Associate Professor of Mathematics at the University of Zagreb in 2000, and to the rank of Full Professor in 2004. He was visiting professor at Technische Universität Graz (in 2001), University of Debrecen (in 2007) and Basque Center for Applied Mathematics Bilbao (in 2011). He mentored 13 PhD theses and more than 170 diploma theses.

He is a member of Croatian Mathematical Society, American Mathematical Society, The Fibonacci Association and International Association for Cryptologic Research. He is the Editor-in-Chief of scientific journals “Glasnik Matematički” and “Rad HAZU, Matematičke znanosti”. His main field of research is number theory, in particular Diophantine equations and elliptic curves. He authored and co-authored more than 100 publications in peer reviewed journals and gave lectures at more than 50 international scientific conferences.

Since May 2012, he is a Full member of the Croatian Academy of Sciences and Arts, and since January 2015 he is Secretary of the Department of Mathematical, Physical and Chemical Sciences and member of the Presidency of the Croatian Academy of Sciences and Arts.

- Website: Link

## Professor Dražen Adamović

#### Professor

**Position:**

• Professor of Mathematics at the Faculty of Science University of Zagreb (Department of Physics)

**Fields of interest:**

• Vertex algebras, infinite-dimensional Lie algebras and superalgebras, conformal field theory

**Awards:**

• Award of the Croatian Academy of Sciences and Arts in 2012

• National science award for natural science in 2009

**Five selected publications:**

• D. Adamović, V. G. Kac, P. Moseneder-Frajria, P. Papi, O. Perše, Finite vs infinite decompositions in conformal embeddings, Communications in Mathematical Physics (2016).

• D. Adamović, R. Lu, K. Zhao, Whittaker modules for the affine Lie algebra , Advances in Mathematics 289 (2016) 438-479

• D. Adamović, A. Milas, On the triplet vertex algebra W(p), Advances in Mathematics 217 (2008) 2664-2699

• D. Adamović, Lie superalgebras and irreducibility of – modules at the critical level, Communications in Mathematical Physics 270 (2007) 141-161

• D. Adamović, Rationality of Neveu-Schwarz vertex operator superalgebras, International Mathematics Research Notices (1997), 865-875

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

• 2014-2018 Principal investigator of the project Algebraic and combinatorial methods in vertex algebra theory, funded by the Croatian Science Foundation, HRZZ

• 2015-2020 member of Scientific centre of excellence QuantiXLie

• 2009-2011 Principal investigator (with. G. Bohm) of Croatian-Hungarian project Algebraic methods in mathematical physics

• 2013-2014, 2016 Principal investigator of two grants of University of Zagreb

• 1998-2003 Principal investigator of grant Vertex-algebras for young scientists, MZOS

**Bio:**

Dražen Adamović received a PhD in mathematics from the University of Zagreb in 1996. He has been promoted to the rank of Associate Professor of Mathematics at the University of Zagreb in 2002, and to the rank of Full Professor in 2007. His main fields of research are the theory of vertex algebras and the representation theory of infinite-dimensional Lie algebras. He published 44 research papers. He was invited speaker on international conferences in Notre Dame, Banff, Beijing, Chengdu, Galway, Pisa, Chenai, Allahabad, Bangalore, Sendai, Vienna, New Orleans and others. He is a member of Croatian Mathematical Society and American Mathematical Society. He is Managing Editor of the scientific journal “Glasnik matematički” and member of editorial boards of j “European Journal of Mathematics”, “Central European Journal of Mathematics” and “Mathematical Communications”. He is one of the organizers of five confererences on Representation Theory in Dubrovnik.