Ivan Matić
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Representation theory of padic groups
 Langlands program
 Theta correspondence
Degrees
 PhD in theoretical mathematics, Department of Mathematics, University of Zagreb , 2010.
 BSc in Mathematics and Computer Science Education, Department of Mathematics, University of Osijek, 2010.
 BSc in Mathematics, Department of Mathematics, University of Zagreb, 2004.
Publications
 I. Matić, Aubert duals of discrete series: the first inductive step, Glasnik Matematički 54/1 (2019), 133178Let $G_n$ denote either symplectic or odd special orthogonal group of rank $n$ over a nonarchimedean local field $F$. We provide an explicit description of the Aubert duals of irreducible representations of $G_n$ which occur in the first inductive step in the realization of discrete series representations starting from the strongly positive ones. Our results might serve as a pattern for determination of Aubert duals of general discrete series of $G_n$ and should produce an interesting part of the unitary dual of this group. Furthermore, we obtain an explicit form of some representations which are known to be unitarizable.
 I. Matić, Aubert duals of strongly positive discrete series and a class of unitarizable representations, Proceedings of the American Mathematical Society 145/8 (2017), 35613570Let G_n denote either the group Sp(n, F) or SO(2n + 1, F) over a local nonarchimedean field F. We explicitly determine the Aubert duals of strongly positive discrete series representations of the group G_n. This enables us to construct a large class of unitarizable representations of this group.
 I. Matić, Composition factors of a class of induced representations of classical padic groups, Nagoya Mathematical Journal 227 (2017), 1648We study induced representations of the form $delta_1 times delta_2 rtimes sigma$, where $delta_1, delta_2$ are irreducible essentially squareintegrable representations of general linear group and $sigma$ is a strongly positive discrete series of classical $p$adic group, which naturally appear in the nonunitary dual. Employing certain conditions on $delta_1$ and $delta_2$, we determine complete composition series of such induced representation.
 I. Matić, On Langlands quotients of the generalized principal series isomorphic to their Aubert duals, Pacific Journal of Mathematics 289/2 (2017), 395415We determine under which conditions is the Langlands quotient of an induced representation of the form $delta rt sigma$, where $delta$ is an irreducible essentially squareintegrable representation of a general linear group and $sigma$ is a discrete series representation of the classical $p$adic group, isomorphic to its Aubert dual.
 I. Matić, On Jacquet Modules of Discrete Series: the First Inductive Step, Journal of Lie Theory 26/1 (2016), 135168The purpose of this paper is to determine Jacquet modules of discrete series which are obtained by adding a pair of consecutive elements to the Jordan block of an irreducible strongly positive representation such that the $epsilon$function attains the same value on both elements. Such representations present the first inductive step in the realization of discrete series starting from the strongly positive ones. We are interested in determining Jacquet modules with respect to the maximal standard parabolic subgroups, with an irreducible essentially squareintegrable representation on the general linear part.
 I. Matić, First occurrence indices of tempered representations of metaplectic groups, Proceedings of the American Mathematical Society 144/7 (2016), 31573172We explicitly determine the first occurrence indices of tempered representations of metaplectic groups over a nonarchimedean local field of characteristic zero with odd residual characteristic.
 I. Matić, On discrete series subrepresentations of the generalized principal series, Glasnik Matematički 51/1 (2016), 125152We study a family of the generalized principal series and obtain necessary and sufficient conditions under which the induced representation of studied form contains a discrete series subquotient. Furthermore, we show that if the generalized principal series which belongs to the studied family has a discrete series subquotient, then it has a discrete series subrepresentation.
 I. Matić, M. Tadić, On Jacquet modules of representations of segment type, Manuscripta Mathematica 147/3 (2015), 437476Let $G_{n}$ denote either the group $Sp(n, F)$ or $SO(2n+1, F)$ over a local nonarchimedean field $F$. We study representations of segment type of group $G_{n}$, which play a fundamental role in the constructions of discrete series, and obtain a complete description of the Jacquet modules of these representations. Also, we provide an alternative way for determination of Jacquet modules of strongly positive discrete series and a description of top Jacquet modules of general discrete series.
 I. Matić, Strongly positive representations in an exceptional rankone reducibility case (an appendix to: 'Strongly positive representations of GSpin_{2n+1} and the Jacquet module method' by Yeansu Kim), Mathematische Zeitschrift 279/12 (2015), 271296We obtain some results on the strongly positive discrete series in an exceptional rankone reducibility case. Such results appear to be important for the classification of strongly positive representations for GSpin groups.
 I. Matić, Strongly positive subquotients in a class of induced representations of classical $p$adic groups, Journal of Algebra 444 (2015), 504526We determine under which conditions the induced representation of the form $delta_{1} times delta_{2} rtimes sigma$, where $delta_{1}, delta_{2}$ are irreducible essentially square integrable representations of a general linear group and $sigma$ is a discrete series representation of classical $p$adic group, contains an irreducible strongly positive subquotient.
 I. Matić, Discrete series of metaplectic groups having generic theta lifts, Journal of the Ramanujan Mathematical Society 29/2 (2014), 201219We prove that a discrete series representations of metaplectic group over a nonarchimedean local field has a generic theta lift on the split odd orthogonal tower if and only if it is generic. Also, we determine the first occurrence indices of such representations and describe the structure of their theta lifts.
 I. Matić, Jacquet modules of strongly positive representations of the metaplectic group $widetilde{Sp(n)}$, Transactions of the American Mathematical Society 365 (2013), 27552778Strongly positive discrete series represent a particularly important class of irreducible squareintegrable representations of $p$adic groups. Indeed, these representations are used as basic building blocks in known constructions of general discrete series. In this paper, we explicitly describe Jacquet modules of strongly positive discrete series. The obtained description of Jacquet modules, which relies on the classification of strongly positive discrete series given in our previous work, is valid in both classical and metaplectic case. We expect that our results, besides being interesting by themselves, should be relevant to some potential applications in the theory of automorphic forms, where both representations of metaplectic groups and structure of Jacquet modules play an important part.
 I. Matić, The conservation relation for discrete series representations of metaplectic groups, International Mathematics Research Notices 2013/22 (2013), 52275269Let $F$ denote a nonarchimedean local field of characteristic zero with odd residual characteristic and let $widetilde{Sp(n)}$ denote the rank $n$ metaplectic group over $F$. If $r^{pm}(sigma)$ denotes the first occurrence index of the irreducible genuine representation $sigma$ of $widetilde{Sp(n)}$ in the theta correspondence for the dual pair $(widetilde{Sp(n)},O(V^{pm}))$, the conservation relation, conjectured by Kudla and Rallis, states that $r^{+}(sigma)+r^{}(sigma)=2n$. A purpose of this paper is to prove this conjecture for discrete series which appear as subquotients of generalized principle series where the representation on the metaplectic part is strongly positive. Also, we prove this relation for many tempered but nonsquare integrable and nontempered irreducible subquotients of such representations. Assuming the basic assumption, we prove the conservation relation for general discrete series of metaplectic groups.
 I. Matić, Theta lifts of strongly positive discrete series: the case of ($widetilde{Sp(n)}$, O(V)), Pacific Journal of Mathematics 259/2 (2012), 445471Let $F$ denote a nonarchimedean local field of characteristic zero with odd residual characteristic. Using the results of Gan and Savin, in this paper we determine the first occurrence indices and theta lifts of strongly positive discrete series representations of metaplectic groups over $F$ in terms of our recent classification of this class of representations. Also, we determine the first occurrence indices of some strongly positive representations of odd orthogonal groups.
 I. Matić, Strongly positive representations of metaplectic groups, Journal of Algebra 334 (2011), 255274In this paper, we obtain the classification of irreducible strongly positive squareintegrable genuine representations of metaplectic groups over $p$adic fields, using purely algebraic approach. Our results parallel those of M{oe}glin and Tadi'{c} for classical groups, but their work relies on certain conjectures. On the other side, our results are complete and there are no additional conditions or hypothesis. The important point to note here is that our results and technics can be used in the case of classical $p$adic groups in completely analogous manner.
 F.M. Brueckler, I. Matić, The power and the limits of the abacus, Mathematica Pannonica 22/1 (2011), 2548The abacus is a wellknown calculating tool with a limited number of placeholders for digits of operands and results. Given a number of rods $n$ of the abacus, a chosen basis of the number system and the first operand $a$, this paper deals with the possible values of the other operand $b$ in the four basic arithmetic operations performed with integers on the abacus. For division we identify several subcases, depending on $n$ and the number of digits $delta_B(a)$ of $a$. If $a$ cannot be divided by all $bleq a$, the number $delta_B(a)$ is called critical. For numbers with the minimal critical number of digits $N_n=lfloorfrac{n4}{3}rfloor+1$ we explicitly determine the values of the maximal divisor $b_{max}$ such that the division $a:b_{max}$ can be performed.
 I. Matić, Composition series of the induced representations of SO(5) using intertwining operators, Glasnik Matematički 45/1 (2010), 93107Let $F$ be a padic field of characteristic zero. We determine the composition series of the induced representations of $SO(5,F)$.
 M. Hanzer, I. Matić, Irreducibility of the unitary principal series of $p$adic $widetilde{Sp(n)}$, Manuscripta Mathematica 132 (2010), 539547Let $F$ be a padic field. We prove irreducibility of the unitary principal series of the group $widetilde{Sp(n)}$ over $F$.
 M. Hanzer, I. Matić, The unitary dual of $p$adic $widetilde{Sp(2)}$, Pacific Journal of Mathematics 248/1 (2010), 107137We investigate the composition series of the induced admissible representations of the metaplectic group $widetilde{Sp(2)}$ over a $p$adic field $F.$ In this way, we determine the nonunitary and unitary duals of $widetilde{Sp(2)}$ modulo cuspidal representations.
 I. Matić, The unitary dual of $p$adic SO(5), Proceedings of the American Mathematical Society 138/2 (2010), 759767Let $F$ be a padic field of characteristic zero. We investigate the composition series of the parabolically induced representations of SO(5,F) and determine the noncuspidal part of the unitary dual of $SO(5,F)$.
 I. Matić, Levi subgroups of $p$adic Spin(2n+1), Mathematical Communications 14/2 (2009), 223233We explicitly describe Levi subgroups of odd spin groups over algebraic closure of a padic field.
 Y. Kim, I. Matić, Classification of Strongly Positive Representations of Even General Unitary Groups, Representations of Reductive padic Groups, Pune, India, 2019, 161174
 A. Katalenić, Lj. Jukić Matić, I. Matić, Approaches to learning mathematics in engineering study program, Mathematics and children, 4th International Scientific Colloquium, Osijek, Hrvatska, 2013, 186195
 Lj. Jukić Matić, I. Matić, Educating future mathematics teachers: Repeating mathematics from primary and secondary school, Mathematics and children, 3rd International Scientific Colloquium, Osijek, Hrvatska, 2011, 2734
 Lj. Jukić Matić, I. Matić, Crtice iz tramvaja zvanog ludara, Osječki matematički list 18/1 (2018), 5969Matematički zadatci uz priču
 I. Matić, Lj. Jukić Matić, Dnevnik malog Medića, Osječki matematički list 17/1 (2017), 8994
 Lj. Jukić Matić, I. Matić, Tri Medića i beba, Osječki matematički list 17/2 (2017), 171176
 Lj. Jukić Matić, I. Matić, Obitelj Medić u posjetu zoološkom vrtu, Osječki matematički list 16/1 (2016), 9398
 I. Matić, Lj. Jukić Matić, Shopping, Osječki matematički list 16/2 (2016), 9194
 Lj. Jukić Matić, I. Matić, Ključevi, Osječki matematički list 15/2 (2015), 6067
 Lj. Jukić Matić, I. Matić, Lov na blago, Osječki matematički list 15/1 (2015), 9598
 Lj. Jukić Matić, I. Matić, M. Pavlović, Geometrija i Sherlock Holmes, Matematika i škola 75 (2014), 195201
 Lj. Jukić Matić, I. Matić, Obitelj Medić se priprema za odlazak u svatove, Osječki matematički list 14 (2014), 169174Zanimljivi zadatci uklopljeni u priču o obitelji Medić.
 M. Libl, I. Matić, Plimpton 322, Matematika i škola 73 (2014), 114118
 Lj. Jukić Matić, I. Matić, Priprema za državnu maturu obitelji Medić, Osječki matematički list 14/1 (2014), 7781
 Lj. Jukić Matić, I. Matić, Gozba obitelji Medić, Osječki matematički list 13/2 (2013), 191194
 Lj. Jukić Matić, I. Matić, Ljetovanje obitelji Medić, Osječki matematički list 13/1 (2013), 8490
 Lj. Jukić Matić, I. Matić, Put djeda mraza, Osječki matematički list 13/1 (2013), 101105
 S. Bingulac, I. Matić, Kineski teorem o ostatcima za polinome, Osječki matematički list 12/2 (2012), 105126
 Lj. Jukić Matić, I. Matić, Role of the competitions in the curricula of teaching computer science, Croatian Journal of Education 13/3 (2011), 201231
 D. Ševerdija, I. Matić, Grčko  kineski stil u teoriji brojeva, Osječki matematički list 10/1 (2010), 4358
 D. Ševerdija, I. Matić, Metodički aspekti abakusa II, Matematika i škola 53 (2010), 106111
 D. Ševerdija, I. Matić, Metodički aspekti abakusa I, Matematika i škola 52 (2009), 5762
 I. Matić, D. Ševerdija, S. Škorvaga, Numerička ograničenja kineskog abakusa, Osječki matematički list 9 (2009), 7591We present some aspects of numerical constraints using chinese abacus in standard arithmetic operations with natural numbers.
 I. Matić, Modalna logika i Fittingova nomenklatura, Poučak 36 (2008)
 Lj. Jukić Matić, I. Matić, Priručnik za nastavu matematike, Odjel za matematiku, Sveučilište J.J. Strossmayera, Osijek, 2017.
 I. Matić, Uvod u teoriju brojeva, Sveučilište Josipa Jurja Strossmayera u Osijeku  Odjel za matematiku, Osijek, 2015.
 Y. Kim, B. Liu, I. Matić, Degenerate principal series in the general case (2019)
 I. Matić, Reducibility of representations induced from the Zelevinsky segment and discrete series (2018)
 I. Matić, Representations induced from the Zelevinsky segment and discrete series in the halfintegral case (2018)
 Y. Kim, I. Matić, Discrete series of odd general spin groups (2017)
Projects
 Composition series of induced representations of classical padic groups (Project run in 2015, supported by University of Osijek.)
 Bilateral project Croatia  Austria: Cohomology of arithmetic groups and automorphic forms (Project leaders: Neven Grbac and Joachim Schwermer)

Discrete series in generalized principal series
(Project run in 2013/14, supported by University of Osijek.)

Automorphic forms, representations and applications
(Project leader: Goran Muić. Project was funded in 2014 by the Croatian Science Foundation.)
 Unitary representations and automorphic forms
(Project leader: Marko Tadić. Project was funded in 2008 by the Croatian Science Foundation.)  Unitary representations, automorphic and modular forms (Project leader: Marcela Hanzer. Project was funded in 2018 by the Croatian Science Foundation.)
Professional Activities
Editorial BoardsCommittee Memberships
Member of American Mathematical Society (AMS) and Croatian Mathematical Society (HMD)
Refereeing/Reviewing
Zentralblatt MATH (since 2010)
Mathematical Reviews (since 2011)
Service Activities
Član povjerenstava za stručnu prosudbu udžbenika iz matematike za osnovnu i srednju školu, 2013./2014.
Predavač na 3. stručnometodičkom skupu Nastava matematike i izazovi moderne tehnologije udruge Normala, s predavanjem na temu Brojevni sustavi.
Član skupine ocjenjivača koja je odredila rang prolaznosti na državnoj maturi iz matematike u 2009./2010. godini.
Festival znanosti:
2009. radionica  Abakus, prvo računalo
2010. radionica  Kako sakriti poruku od ostatka Zemlje?
2011. radionica  Pobjedničke strategije
2012. predavanja  Brojevni sustavi
2014. radionica  Što ako netko otkrije valove vaših poruka?
Član izvršnog odbora Udruge matematičara Osijek
Zimska škola matematike:
2005. predavanje  Fibonaccijevi brojevi
2010. radionica  O jednom zaboravljenom pomagalu pri računanju
Coolmath (V. gimnazija Zagreb):
2010. radionica  Kako i zašto raditi na abakusu
Teaching
Nastavne aktivnosti u akademskoj godini 2014./2015.:
Kriptografija i sigurnost sustava
Učenička matematička natjecanja
Matematika 1 (Građevinski fakultet)
Matematika 2 (Građevinski fakultet)
Nastavne aktivnosti u prošlosti:
Uvod u teoriju brojeva  udzbenik
Konzultacije (Office Hours): Po dogovoru.
Teme diplomskih i završnih radova.
Mentorstva diplomskih i završnih radova.
Links
Math links:
Seminar za unitarne reprezentacije i automorfne forme
Colleagues:
Personal