### Members of the Lie unit

## Prof. Ozren Perše

#### Prof.

**Position:**

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

**Fields of interest:**

Vertex algebras, infinite-dimensional Lie algebras, conformal field theory

**Awards:**

Croatian Mathematical Society award for scientific achievements in mathematics in 2008

**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 348 (2016), 445-473.
- D. Adamović, O. Perše, Fusion rules and complete reducibility of certain modules for affine Lie algebras, Journal of algebra and its applications 13 (2014) 1350062 18pp.
- D. Adamović, O. Perše, Some general results on conformal embeddings of affine vertex operator algebras, Algebras and representation theory 16 (2013) 51-64.
- D. Adamović, O. Perše, The vertex algebra M(1)^+ and certain affine vertex algebras of level -1, SIGMA 8 (2012) 040 16 pp.
- O. Perše, Vertex operator algebras associated to type affine Lie algebras on admissible half-integer levels, Journal of Algebra 307 (2007), 215-248.

**Bio:**

Ozren Perše received a PhD in mathematics from the University of Zagreb in 2005. (supervisors: D. Adamović and M. Primc). He has been promoted to the rank of Associate Professor of Mathematics at

University of Zagreb in 2013. His main fields of research are the theory of vertex operator algebras and infinite-dimensional Lie algebras. He is an author of 11 research papers. He gave around 20 lectures at conferences, and participated as a researcher in several scientific grants. He taught many undergraduate and post-graduate courses. He supervised one PhD thesis and 20 diploma thesis.

## Prof. Boris Širola

**Position:**

- Professor of mathematics at the Department of Mathematics, University of Zagreb

**Fields of interest:**

- Lie algebras and algebraic groups, and their representations; algebraic and geometric aspects
- Noncommutative algebra, algebraic number theory

**Five selected publications:**

- Širola,
*Distinguished nilpotent orbits, Kostant pairs and normalizers of Lie algebras*, J. Algebra 423 (2015), 636-682. - Širola,
*Compatible pairs of Borel subalgebras and shared orbit pairs*, J. Algebra 423 (2015), 726-766. - Širola,
*On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras,*Proc. Amer. Math. Soc. 141 (2013), 2233-2243. - Širola,
*On noncommutative Noetherian schemes*, J. Algebra 282 (2004), 667-698. - Širola,
*On supports and associated primes of modules over the enveloping algebras of nilpotent Lie algebras,*Trans. Amer. Math. Soc. 353 (2001), 2131-2170.

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

- 2007-2013 Principal investigator at the project
*Enveloping algebras of Lie algebras and their modules*(no. 900-194134), funded by the Ministry of Science, Education and Sport in Croatia. - 2002-2006 Principal investigator at the project
*Restriction of representations of semisimple Lie groups and Lie algebras*(no. 0037121), funded by the Ministry of Science and Technology in Croatia. - 2000-2002 Principal investigator at the supporting project for young scientists
*Characteristic cycles and embedding of modules for enveloping algebras*(no. 037057), funded by the Ministry of Science and Technology in Croatia.

**Vita:**

Boris Širola earned a B.Sc. degree in mathematics at the Department of Mathematics, University of Zagreb, in 1988. He also earned a M.Sc. degree in 1992. and Ph.D. in 1996., at the same institution.

He held a position of a teaching assistant at the Department of Mathematics, University of Zagreb, since 1988. He received a permanent position of Assistant Professor in 2000., and was promoted to the rank of Associate Professor in 2005., and to the rank of Professor in 2012. An academic year 1998./99. he spent as a postdoc at the Massachusetts Institute of Technology, Cambridge, MA, USA. He has also been, as a visiting scholar, at the following institutions: Tata Institute of Fundamental Research, Mumbai (2002.); Mathematische Institut, Heinrich Heine Universitet, Dusseldorf (2005.); University of Utah, Salt Lake City (2010. i 2014.) His fields of interest are (noncommutative) algebra, group theory, number theory and mostly Lie theory; in particular, structure theory and representation theory of Lie algebras, some problems related to investigations of geometry of nilpotent orbits and flag varieties for reductive groups, and relationship with representation theory of algebraic groups. As an only author he published 21 scientific papers in recognized mathematical journals; some of them in leading journals specialized for algebra.

At the undergraduate study he held several courses (e.g., Algebraic structures, Theory of analytic functions). At the graduate study he created and held 4 two-semester courses (Lie algebras and representation theory, Commutative algebra, Riemann Zeta function and Introduction to the theory of analytic functions of several complex variables). He is a cofounder and coleader of the Seminar for Algebra at the University of Zagreb.

## Marijana Butorac

**Position:**

- Postdoctoral Research/Senior Assistant of Department of Mathematics at the University of Rijeka

**Fields of interest:**

- Infinite dimensional Lie algebras
- Vertex algebras
- Rogers-Ramanujan type identities

**Awards: ** –

**Five selected publications:**

- M. Butorac,
*Quasi-particle bases of principal subspaces of the affine Lie algebra of type*, accepted for publication in Glasnik Matematicki - M. Butorac,
*Quasi-particle bases of principal subspaces for the affine Lie algebras of types**and ,*Glasnik Matematicki, Vol. 51, No.1 (2016).

- Butorac,
*Combinatorial bases of principal subspaces for the affine Lie algebra of type*, J. Pure Appl. Algebra 218, No. 3 (2014).

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

**Bio:**

Marijana Butorac received a BSc degree in Mathematics and Physics from the Faculty of Humanities and Social Sciences, University of Rijeka (supervisor: Prof. Rajka Jurdana-Šepić) in 2005. In 2012 she defended her PhD thesis at the Faculty of Science, University of Zagreb (supervisor: Prof. Mirko Primc).

Since 2012 she works as a senior assistant at the Department of Mathematics, University of Rijeka. Prior to this, she worked as an assistant at the Department of Mathematics, University of Rijeka and at the Department of Mathematics, Faculty of Art and Sciences Rijeka and before that as a teacher of mathematics and physics at the “ Istituto professionale Buje” in Buje and at the elementary school “Gornja Vežica” in Rijeka.

She is a member of “Scientific Center of Excellence for Quantum and Complex Systems – QuantiX” and “Algebraic and combinatorial methods in vertex algebra theory” Croatian Science Foundation research project.

## Prof. Domagoj Kovačević

- Website: Link

#### Assistant Professor

**Position:**

- Assistant Professor at Faculty of Electrical Engineering and Computing

**Fields of interest:**

- Representation Theory
- Mathematical Physics

**Five selected publications:**

- D. Kovačević, S. Meljanac, A. Samsarov, Z. Škoda, Hermitian realizations of kappa-Minkowski spacetime, International journal of modern physics A 30 (2015) 1550019-1-1550019-26.
- T. Jurić, D. Kovačević, S. Meljanac, Kappa-deformed phase space, Hopf algebroid and twisting, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) (1815-0659) 10 (2014); 106-124.
- D. Kovačević, S. Meljanac, A. Pachol, R. Štrajn, Generalized Poincaré algebras, Hopf algebras and kappa-Minkowki spacetime, Physics Letters B 711 (2012) 122-127.
- D. Kovačević, S. Meljanac, Kappa-Minkowski spacetime, kappa-Poincaré Hopf algebra and realizations, J. Phys. A: Math. Theor. 45 (13) (2012) 135208.
- D. Kovačević, Real forms of dual pairs g2xh in g of type E6, E7 and E8, Journal of Lie theory 21(2) (2011) 417-426.

**The most important grants:**

- 2015- Member of the Scientific Center of Excellence for Quantum and Complex Systems – QuantiX
- 2009-2013 – Member of the project Quantum field theory, noncommutative spaces and symmetries funded by MZOS<

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**Bio:**

Domagoj Kovačević was born on January 14, 1968 in Požega, Croatia. He graduated from the High School in Zagreb. In 1986, he won bronze medal at the International Mathematical Olympiad in Poland. After the military service, he enrolled at the Department of Mathematics at the University of Zagreb. In 1993, he graduated and was enrolled as a PhD student at the University of Utah. His major interest during the graduate study was representation theory. In 2000, he came back and started to teach mathematics in XV. High School. In 2006, he defended his PhD thesis at the University of Utah. The thesis advisor was professor Gordan Savin. After that, Domagoj Kovačević became a Senior Instructor at the Faculty of Electrical Engineering and Computing at the University of Zagreb and started research collaboration with professor Stjepan Meljanac from Ruđer Bošković Intitute, where five papers were produced. In 2012, he became an Assistant Professor and started doing representation theory again. At the Faculty of Electrical Engineering and Computing he taught several undergraduate courses.

## 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.

## Rafael Mrđen

- Website: Link

#### 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.

## Ana Prlić

- Website: Link

**Position:**

- Postdoctoral researcher at the Faculty of Science University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Representations of semisimple Lie groups and algebras: Dirac operators in representation theory

**Awards:**

- Top scholarship for top students (2007)
- Dean’s award (2005 and 2006)

**Publications:**

- A. Prlić, Algebraic Dirac Induction for Nonholomorphic Discrete Series of SU(2,1), J. Lie Theory 26 (2016), no. 3, 889-910.
- A. Prlić, K-invariants in the algebra U(g) ⊗ C(p) for the group SU(2,1), Glas. Mat. 50 (2015), no. 2, 397-414

**Bio:**

Ana Prlić was born on November 6th, 1983 in Imotski. Under the mentorship of professor Hrvoje Kraljević she achieved a BSc in 2007 with the thesis title “Representations of the three-dimensional Lorentz group”. On May 27th, 2014 she obtained Ph.D. degree with the thesis “Algebraic Dirac induction for discrete series representations of the group SU(n,1)” under the mentorship of professors Hrvoje Kraljević and Pavle Pandžić.

From July 2008 tilI July 2014 she was employed as a teaching assistant at the Department of Mathematics, University of Zagreb. She has been employed as a postdoctoral researcher at the same faculty from July, 2014 till now.

AP authored two publications and gave a talk at four international conferences.

## Professor Mirko Primc

**Position:**

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

**Fields of interest:**

- Representation theory of affine Lie algebras and vertex operator algebras

**Awards:**

- Croatian National Science Award for 1993 for natural sciences
- Award of the Croatian Academy of Sciences and Arts for 2000 for natural sciences

**Five selected publications: **

- J. Lepowsky and M. Primc, Structure of the standard modules for the affine Lie Algebra A1(1), Contemporary Math. 46, AMS, Providence, 1985, 1-84.
- M. Primc, Vertex operator construction of standard modules for An(1), Pacific J. Math. 162 (1994), 143–187.
- A. Meurman and M. Primc, Annihilating fields for standard modules of sl(2, C)~ and combinatorial identities, Memoirs Amer. Math. Soc. 652, AMS, 1999, 1-89.
- M. Primc, Basic representations for classical affine Lie algebras, J. Algebra 228 (2000), 1-50.
- M. Primc, Combinatorial bases of modules for affine Lie algebra B2(1), Cent. Eur. J. Math. 11 (2013), 197-225.

**PI on MZOS grant:**

- Infinite analysis (037002)
- Vertex operator algebras and infinite dimensional Lie algebras (037-0372794-2806)

**CV:**

Mirko Primc received a BSc degree in physics from the University of Zagreb in 1971 and defended his PhD thesis in mathematics at the same university in 1978. Since 1979 he is an assistant professor, since 1986 an associate professor and since 1993 a full professor at the University of Zagreb. Academic year 1980/81 he was a member at the Institute for Advanced Study in Princetonu, USA, academic year 1983/84 he was a member at the Mathematical Sciences Research Institute in Berkeley, USA, and in academic year 1991/92 he visited Department of Mathematics at the University of Lund, Sweden.

He mentored nine PhD theses and a number of BSc and MSc theses.

## Professor Hrvoje Kraljević

**Position:**

- Retired full professor at the Department of Mathematics, Faculty of Science, University od Zagreb

**Education:**

- PhD in Mathemacs on February 28, 1973, Faculty of Science, University of Zagreb, with dissertation „Representations of the Group SU(n,1) and of Its Universal Covering Group“, mentor Svetozar Kurepa
- MSc in Mathematics on November 6, 1968, Faculty of Science, University of Zagreb, with thesis „Induced Representations of Locally Compact Groups and Some Applications“, mentor Svetozar Kurepa
- Bachelor’s degree in Theoretical Physics on November 16, 1966, Faculty of Science, University of Zagreb, with thesis „Group Representations and Applications in the Theora of Symmetries of Elemetary Particles“, mentor Svetozar Kurepa
- completed secondary schooling 1962 at the Classical Gymnasium in Zagreb

**Academic career:**

- 1966–1973 Assistant, Department of Mathematics, Faculty of Science, University of Zagreb
- 1973–1976 Assistant Professor (Dozent), Department of Mathematics, Faculty of Science, University of Zagreb
- 1976–1981 Associate Professor, Department of Mathematics, Faculty of Science, University of Zagreb
- from 1981 Full Professor, Department of Mathematics, Faculty of Science, University of Zagreb
- from 1990 Full Professor with tenure, Department of Mathematics, Faculty of Science, University of Zagreb

**Specializations:**

- February 1997, Institut für Mathematik der Universität „Karl Franzens“ Graz, Austria
- March 1981, Libera Università degli Studi, Trento, Italy
- March 1979, Libera Università degli Studi, Trento, Italy
- March–April 1978, École Polytechnique, Palaiseau, France
- 1974/75 Institute for Advanced Study, Princeton, USA

**Fields of interest:**

- Representation theory of Lie grouops and algebras
- Banach algebras, C*–algebras
- Operator theory on Hilbert spaces

**Five selected publications:**

- Kraljević, Representations of the universal covering group of the group SU(n,1), Glasnik Mat. 8(28) (1973), 23-72.
- Kraljević, On representations of the group SU(n,1), Trans. Amer. Math. Soc. 221(1976) (1976), 433-448.
- Kraljević, A note on nonunitary principal series representations, Proc. Amer. Math. Soc. 70 (1978), 213-216.
- Baldoni Silva, H.Kraljević, Composition factors for the principal series representations of the groups Sp(n,1), Trans. Amer. Math. Soc. 262 (1980), 447-471.
- Kraljević,S.Suljagić, K.Veselić, Index in semisimple Banach algebras, Glasnik Mat. 17(37) (1982), 73-95.

**Scientific grants (as principal investigator):**

- 2008–2014 a project of the Croatian Ministry of science, education and sports, code 037–0372794–3229, title „Representations of semisimple Lie groups; K–types, duals, C*–algebras“
- 1997–2001 a project of the Croatian Ministry of science and technology, code 037003, title „Functionalnoanalytic, geometric and algebraic aspects of representation theory of real Lie groups“
- 1993–1996 a project of the Croatian Ministry of science and technology, code 1–01–251, title „Representation theory“

**Scientific grants (as colaborator):**

- From December 11, 2015 the Croatian Scientific Center of Excelence for Quantum, and Complex Sistems and Repesentations of Lie Algebras (principal investigators Hrvoje Buljan and Pavle Pandžić)
- From June 1, 2014 a project of the Croatian Scientific Foundation „Dirac Operators in Representation Theory“ (principal investigator Pavle Pandžić)
- 2011–2012 and 2013–2014 Croatian–French bilateral scientific project Cogito (principal investigators Pavle Pandžić and Salah Mehdi)
- 2002–2007 a projekt of the Croatian Ministry of science and technology, code 0037106, title „Hilbert Modules and Operator Spaces“ (principal investigator Boris Guljaš)

**Awards and tributes:**

- March 2014. Honorary Doctorate from the University of Zadar
- from 1992 corresponding member of the Croatian Academy of Sciences and Arts
- 1987 honorary advisor of the University of Osijek
- 1984 Croatian anual award „Ruđer Bošković“ for scientific discovery
- 1973 award of the Balkan Mathematical Union for young scientists
- 1970 award „Seven SKOJ secretaries“ for young scientists
- 1965 rector’s award of the University of Zagreb

**Director of scientific conferences:**

- 2015 „Representation Theory XIV“, IUC, Dubrovnik
- 2013 „Representation Theory XIII“, IUC, Dubrovnik
- 2011 „Representation Theory XII“, IUC, Dubrovnik
- 2009 „Representation Theory XI“, IUC, Dubrovnik
- 2008 „Functional Analysis X“, IUC, Dubrovnik
- 2005 „Functional Analysis IX“, IUC, Dubrovnik
- 2004 „XI Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 2003 „Functional Analysis VIII“, IUC, Dubrovnik
- 2001 „Functional Analysis VII“, IUC, Dubrovnik
- 2001 „X Mathematikertreffen Zagreb–Graz“, Motovun
- 1999 „Functional Analysis VI“, IUC, Dubrovnik
- 1997 „Functional Analysis V“, IUC, Dubrovnik
- 1995 „IX Mathematikertreffen Zagreb–Graz“, Motovun
- 1993 „Functional Analysis IV“, IUC, Dubrovnik
- 1993 „VIII Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1990 „VII Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1989 „Functional Analysis III“, IUC, Dubrovnik
- 1988 „VI Mathematikertreffen Zagreb–Graz“, Opatija
- 1986 „V Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1985 „Functional Analysis II“, IUC, Dubrovnik
- 1984 „IV Mathematikertreffen Zagreb–Graz“, Mali Lošinj
- 1982 „III Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1981 „Functional Analysis“, IUC, Dubrovnik
- 1980 „II Mathematikertreffen Zagreb–Graz“, Plitvice
- 1978 „Mathematikertreffen Zagreb–Graz“, Retzhoff, Austria

**Biography – other:**

Hrvoje Kraljević was born on March 16, 1944 in Zagreb. After Bachelor’s degree he initiated studying representation theory in Croatia. 1976–1990 editor and 1990–1995 editor–in–chief of the scientific journal “Glasnik matematički”. Member of the Croatian Mathematical Society, the American Mathematical Society and the European Mathematical Society. From 2007 the president of the Croatian Mathematical Society. Mentor of 6 PhD theses, 12 MSc theses and more than 100 Bachelor’s degree theses. Held 22 lectures in scientific conferences (mostly international) and 30 invited colloquium and seminar lectures in different scientific institutions. Held more than 30 different undergraduate courses in Zagreb, Osijek, Dubrovnik and Mostar, and 26 postgraduate courses at the departments of mathematics, physics and civil engineering in Zagreb. Published 29 scientific papers, two university textbooks, two secondary school textbooks and 15 Internet lecture notes. From January 2000 until July 2002. he was Minister of Science and Technology in the Government of the Republic of Croatia.

## Professor Dražen Adamović

- Website: Link

#### 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.

## Andrej Dujella

- Website: Link

#### 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.

## 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.