Unitary Representations and Automorphic Forms Seminar

Seminar za unitarne reprezentacije i automorfne forme

Termin: ponedjeljak 16:00-18:00

Mjesto: PMF-Matematički odsjek, predavaonica 109

Voditelji: N. Grbac, M. Hanzer, I. Matić, G. Muić, M. Tadić

Sljedeći seminar:

25.11.2024., Lovro Greganić, Sveučilište Jurja Dobrile u Puli, Uvod u lokalna polja.

Prošli seminari:

2024/2025

2023/2024

2022/2023

1. 25.09.2023., Igor Ciganović, PMF-MO, Dekompozicija nekih induciranih reprezentacija u slučaju kuspidalne reducibilnosti jedne polovine
2. 18.09.2023., Barbara Bošnjak, PMF-MO, Kriterij ireducibilnosti za reprezentacije inducirane iz Speh i reprezentacija Arthurovog tipa
3. 11.09.2023., Marcela Hanzer, PMF-MO, Arthurovi parametri i theta korespondencija-Adamsova slutnja
4. 22.05.2023., Maarten Solleveld, Radboud University, Nizozemska, Principal series representations of quasi-split p-adic groups Abstract: Kazhdan and Lusztig famously parametrized the Iwahori-spherical representations of split reductive p-adic groups. That can be considered as one of the first instances of the local Langlands correspondence, and as a starting point for the role of affine Hecke algebras in the Langlands program. In this talk we discuss the local Langlands correspondence for all principal series representations of quasi-split reductive p-adic groups, which was established recently. This is a generalization of the Iwahori-spherical case which still bears considerable similarity with that case. However, the proof is in many ways completely different from the work of Kazhdan--Lusztig. For example, in our setting the affine Hecke algebras do not arise from types, and in these algebras different roots may have different q-parameters. We will explain some parts of the proof of the correspondence, in particular how generic representations are used to make it canonical.
5. 15.05.2023., Emile Takahiro Okada, National University of Singapore Abstract: For a reductive group defined over a p-adic field, the wavefront set is an invariant of an admissible representations which roughly speaking measures the direction of the singularities of the character near the identity. Studied first by Roger Howe in the 70s, the wavefront set has important connections to Arthur packets, and has been the subject of thorough investigation in the intervening years. Of the many open questions regarding this invariant, one of main lines of inquiry is to determine the relation between the wavefront and the L-parameter of a representation. In this talk we present new results answering this question for unipotent representations with real infinitesimal character. The results are joint with Dan Ciubotaru and Lucas Mason-Brown.
6. 08.05.2023., Jan Frahm, Aarhus University, Analytic continuation of branching laws for unitary representations Abstract: Branching problems ask for the behaviour of the restriction of an irreducible representation of a group $G$ to a subgroup $H$. In the context of smooth representations of real reductive groups, this typically leads to the study of multiplicities with which an irreducible representation of $H$ occurs as a quotient of an irreducible representation of $G$. Here, both quantitative results such as multiplicity-one theorems and qualitative results such as the Gan-Gross-Prasad conjectures are of interest. In the context of unitary representations of real reductive groups, one can go a step further and explicitly decompose an irreducible representation of $G$ into a direct integral of irreducible representations of $H$. I will explain how branching laws for unitary representations are related to those in the smooth category, and how one can use an analytic continuation procedure along a principal series parameter to obtain explicit branching laws from certain Plancherel formulas for homogeneous spaces.
7. 20.03.2023., Sonja Žunar, Sveučilište u Zagrebu, O jednoj familiji Siegelovih Poincaréovih redova.
8. 13.03.2023., Sonja Žunar, Sveučilište u Zagrebu, Dva pristupa problemu neponištavanja Poincaréovih redova.

2021/2022

1. 24.06.2022., Barbara Bošnjak, PMF-MO, Composition series and unitary subquotients of representations induced from essentially Speh and cuspidal Abstract: In this talk we will consider representations of symplectic or special odd-orthogonal group over a non-archimedean local field. We describe a composition series of a representation induced from essentially Speh and cuspidal representation under certain conditions. Combined with the previous results of the author, we get irreducible unitary representations of considered groups at the ends of complementary series.
2. 23.06.2022., Alberto Minguez, University of Vienna, The explicit Zelevinsky-Aubert involution Abstract: Let F be a local non-archimedian field. In 1980, A. Zelevinsky defined an involution pi -> pi^t in the Grothendieck group of finite length complex smooth representations of GL(n,F) and conjectured that this involution preserves irreducibility. A.-M. Aubert showed that Zelevinsky's definition can be extended to the Grothendieck group of finite length complex smooth representations of any connected reductive p-adic group G and proved that the involution preserves irreducibility. In 1986, C. Moeglin et J.-L. Waldspurger gave an algorithm to compute the Langalnds parameters of pi^t in terms of the parameters of pi in the case where pi is an irreducible representation of GL(n,F). In this talk I will treat the cas where G is the group Sp(2n,F) or SO(2n+1,F). It is a joint work with H. Atobe.
3. 23.06.2022., Igor Ciganović, PMF-MO, Composition series of a class of induced representations built on discrete series Abstract: We give a formula for composition series of a class of induced representations, appearing in Mœglin-Tadi ́c classification of discrete series, when the GL part of the induced representation admits no reducibility, with the respect to the contragredient permutation of involved segments, whose number is not limited.
4. 22.06.2022., Neven Grbac, Sveučilište u Puli, On the Franke filtration Abstract: The Franke filtration is a finite descending filtration of the spaces of automorphic forms on the adelic points of a reductive connected linear algebraic group defined over a number field. It is defined in terms of the main values of derivatives of cuspidal and degenerate Eisenstein series. The main property of the filtration is that the quotients can be described in terms of parabolically induced representations. This talk will provide an overview of the Franke filtration and exhibit the subtleties of the filtration through examples. Parts of this talk are joint work with Harald Grobner.
5. 22.06.2022., Hiraku Atobe, Hokkaido University, Computation of local A-packets in Sage, Abstract:Local A-packets classify the local factors of square-integrable automorphic representations. I gave a reformulation of Moeglin’s explicit construction of local A-packets, and proved several properties of representations of Arthur type. I wrote a Sage code for computing local A-packets and related topics. In this talk, I will explain how to use my program.
6. 21.06.2022., Nadya Gurevich, University of Negev,Gelfand -Graev representation for covering groups and applications Abstract: One obvious contrast between representations of linear and covering groups is the failure of uniqueness of Whittaker model. The functor, associating to every representation the space of Whittaker functionals on it, is represented by the Gelfand-Graev representation V. We study the Iwahori-Hecke algebra module of Iwahori-fixed vectors of V for a covering group G. The projectivity of this module allows us to compute dimensions of Whittaker spaces of constituents of unramified principal series induced from (a) regular (b) unitary characters. This is a joint work with Fan Gao and Edmund Karasiewicz.
7. 21.06.2022., Dubravka Ban, Southern Illinois University, From $GL_2(\mathbf{Q}_p)$ to $SL_2(\mathbf{Q}_p)$, Abstract:Starting with the Colmez $p$-adic Langlands correspondence for $GL_2(\mathbf{Q}_p)$ we will describe the corresponding objects for $SL_2(\mathbf{Q}_p).$
8. 20.06.2022., Arnaud Mayeux, Universite Clermont Auvergne, Around constructions of supercuspidal representations Abstract: I will compare Bushnell-Kutzko and Sécherre's constructions for GL_N and its inner forms to Yu's construction for tame groups. Then I will talk about some related formalisms and constructions (dilatations, congruent Moy-Prasad isomorphism, attractors associated to monoids and roots groups) using Grothendieck's scheme formalism.
9. 20.06.2022., Sonja Žunar, Sveučilište u Zagrebu, On the Schwartz space $(G(k)∖G(𝔸))$ Abstract:On the Schwartz space $ \mathcal S(G(k)\backslash G(\mathbb A))$ Abstract:Let $ G $ be a connected reductive group defined over a number field $ k $ with adele ring $ \mathbb A $. We introduce the Schwartz space $ \mathcal S(G(k)\backslash G(\mathbb A)) $ -- an adelic version of Casselman's Schwartz space $ \mathcal S(\Gamma\backslash G_\infty) $, where $ \Gamma $ is a discrete subgroup of $ G_\infty=\prod_{v\mid\infty}G(k_v) $. The strong dual $ \mathcal S(G(k)\backslash G(\mathbb A))' $ has many intriguing properties, e.g., its (naturally defined) G\aa rding subspace may be identified with the space $ C^\infty_{umg}(G(k)\backslash G(\mathbb A)) $ of smooth functions of uniform moderate growth. We will describe the closed irreducible admissible $ G(\mathbb A) $-invariant subspaces of $ \mathcal S(G(k)\backslash G(\mathbb A))'$ and discuss applications to automorphic forms. This is joint work with Goran Muić.
10. 16.05.2022.Lei Zhang, Department of Mathematics, National University of Singapore, Multiplicities for strongly tempered spherical varieties Abstract: In this talk, we will discuss the local multiplicity formula of strongly tempered spherical subgroups, which have similar properties like Gan-Gross-Prasad conjecture. In particular, we formulate the epsilon dichotomy conjecture for those spherical subgroups and prove this conjecture for the tempered representations of endoscopy type. Globally, the corresponding automorphic periods are related to the central values of certain L-functions. This is a joint project with Chen Wan at Rutgers University—Newark.
11. 28.03.2022., Max Gurevich, Technion, Israel, The Robinson-Schensted-Knuth transform for irreducible representations, Abstract:The RSK algorithm gives a well-known bijection between multisets of pairs of integers and semistandard bitableaux. In a work with Erez Lapid we categorified the RSK transform, by applying it on the multisegments of the Zelevinsky classification for p-adic general linear groups, thus producing a new construction for irreducible smooth representations. I would like to discuss how aspects of this procedure are better understood through the lens of bases in a quantum group and their quiver Hecke algebra categorification. Time permits, I will show how a curious connection between the classical tool of Bernstein-Zelevinsky derivatives for p-adic groups and the Kashiwara crystal for quantum groups, links the RSK picture with that of cyclotomic Hecke algebra representations.
12. 15.02.2022., Damir Mikoč, Sveučilište u Zadru, obrana doktorske disertacije "Generalizirani Wronskiani i modularne krivulje."
13. 07.02.2022., Bin Xu, Yau Mathematical Sciences Center, Tsinghua University, Beijing, Arthur's conjectures for symplectic and orthogonal similitude groups, Abstract:Arthur (1989) conjectured that the discrete spectrum of automorphic representations of a connected reductive group over a number field can be decomposed into A-packets, in terms of which he also conjectured a multiplicity formula. In this talk I will give an introduction to these conjectures and report on the progress for symplectic and orthogonal similitude groups based on the works of Arthur and Moeglin for classical groups.
14. 25.01.2022., Barbara Bošnjak, PMF-MO, obrana doktorske disertacije, Reducibilnosti i kompozicioni nizovi nekih važnih induciranih reprezentacija klasičnih p-adskih grupa.
15. 25.11.2021., Petar Bakić, University of Utah i PMF-MO, Iznimne theta korespondencije.

2020/2021

1. 31.05.2021., Barbara Bošnjak, PMF-MO, Reducibilnosti i kompozicioni nizovi nekih važnih induciranih reprezentacija klasičnih p-adskih grupa (2. dio)
2. 24.05.2021., Barbara Bošnjak, PMF-MO, Reducibilnosti i kompozicioni nizovi nekih važnih induciranih reprezentacija klasičnih p-adskih grupa (1. dio)
3. 17.05.2021., Damir Mikoč, Sveučilište u Zadru, Generalizirani Wronskiani i modularne krivulje 4.
4. 10.05.2021., Damir Mikoč, Sveučilište u Zadru, Generalizirani Wronskiani i modularne krivulje 3.
5. 03.05.2021., Damir Mikoč, Sveučilište u Zadru, Generalizirani Wronskiani i modularne krivulje 2.
6. 26.04.2021., Damir Mikoč, Sveučilište u Zadru, Generalizirani Wronskiani i modularne krivulje 1.
7. 19.04.2021., Erez Lapid, Weizmann Institute of Science, A binary operation on nilpotent varieties of type A. Abstract:Lusztig's canonical bases for the negative part of a quantized universal enveloping algebra are parameterized by irreducible components of nilpotent varieties. In type A, the latter also parameterize, by the work of Bernstein and Zelevinsky, irreducible representations of general linear groups over a non-archimedean local field. We define a binary operation on the set of irreducible components of nilpotent varieties (for any Dynkin diagram) and contemplate its representation-theoretic significance for GL_n(F). Some results in this direction are given. Joint work with Alberto Minguez and Avraham Aizenbud. https://arxiv.org/abs/2103.12027.
8. 12.04.2021., Harald Grobner,University of Vienna, Deligne’s conjecture for automorphic motives over CM-fields Abstract: In 1979 Deligne conjectured that the critical values of a motivic L-function can be expressed as the algebraic multiple of a certain period, which is nothing else than a determinant, and some explicit powers of 2*pi*i. For motives attached to conjugate self-dual cuspidal automorphic representations of GL(n) over a CM-field Deligne’s conjecture is now a theorem, due to recent work of the speaker jointly with Michael Harris and Jie Lin. Still, our result depends on several assumptions on our automorphic representations in question and on the validity of two very well-expected conjectures, which we will explain in this talk.
9. 29.03.2021., Gordan Savin, University of Utah, Geometry of exceptional groups
10. 11.01.2021., Damir Mikoč, Sveučilište u Zadru, Generalizirani Wronskiani i modularne krivulje
11. 16.11.2020., Ivana Vukorepa, PMF-MO, Uvod u p-adske brojeve i adele

2019/2020

1. 21.09.2020., Josip Novak, Fakultet strojarstva i brodogradnje, Automorfne forme i reprezentacije.
2. 13.07.2020., Veronika Pedić, PMF-MO, Od klasičnih modularnih formi do automorfnih formi.
3. 15.06.2020., Barbara Bošnjak, PMF-MO, Operatori ispreplitanja
4. 08.06.2020., Sonja Žunar, PMF-MO, Vektorski Poincaréovi redovi II
5. 25.05.2020., Igor Ciganović, PMF-MO, Dekompozicija nekih induciranih reprezentacija II
6. 18.05.2020., Igor Ciganović, PMF-MO, Dekompozicija nekih induciranih reprezentacija.
7. 13.01.2020., Sonja Žunar, PMF-MO, Vektorski Poincaréovi redovi.
8. 18.11.2019., Barbara Bošnjak, PMF-MO, obrana teme doktorske disertacije Reducibilnosti i kompozicioni nizovi nekih važnih induciranih reprezentacija klasičnih p-adskih grupa.

2018/2019

05.09.2019. Projektni sastanak projekta IP-2018-01-3628 (Unitarne reprezentacije, automorfne i modularne forme):
1. Sonja Žunar, PMF-MO, Schwartzov prostor, automorfne forme i Poincareovi redovi na G(k)\G(A)
2. Darija Brajković, Odjel za matematiku, Osijek, Unitarni dual p-adske grupe SO(7) s nosačem na miśimalnoj paraboličkoj podgrupi
3. Ivan Matić, Odjel za matematiku, Osijek, O metodama determinacije kompozicionih nizova.
4. Goran Muić, PMF-MO, O idealima koji definiraju ireducibilne reprezentacije reduktivnih p-adskih grupa
5. Igor Ciganović, PMF-MO, Kompozicioni nizovi nekih induciranih reprezentacija
6. Barbara Bošnjak, PMF-MO, Kompozicioni nizovi reprezentacije $Speh\rtimes\sigma$
7. Marcela Hanzer, Petar Bakić, PMF-MO, Generalizirana injektivnost, generičke reprezentacije metaplektičke grupe; theta korespondencija
8. 17.06.2019., Obrana doktorske disertacije Darije Brajković, Odjel za matematiku, Sveučilište u Osijeku, Unitarni dual p-adske grupe SO(7) s nosačem na minimalnoj paraboličkoj podgrupi
9. 10.06.2019., Dubravka Ban, Southern Illinois University Carbondale,"Projektivne kristabelinske reprezentacije i pridružene Banachove reprezentacije".
10. 03.06.2019., Sonja Žunar, PMF-MO, Schwartzov prostor $\mathcal S(G(k)\backslash G(\mathbb A))$ III
11. 27.05.2019., Sonja Žunar, PMF-MO, Schwartzov prostor $\mathcal S(G(k)\backslash G(\mathbb A))$ II.
12. 20.05.2019., Sonja Žunar, PMF-MO, Schwartzov prostor $\mathcal S(G(k)\backslash G(\mathbb A)).$
13. 15.04.2019. Marcela Hanzer, PMF-MO, Eisensteinovi redovi povezani s Jordanovim algebrama.
14. 25.02.2019., Barbara Bošnjak, PMF-MO, Reducibilnost parabolički induciranih reprezentacija II.
15. 18.02.2019., Barbara Bošnjak, PMF-MO, Reducibilnost parabolički induciranih reprezentacija I.
16. 29.10.2018., Petar Bakić, PMF-MO, obrana doktorske disertacije, "Theta liftovi ireducibilnih reprezentacija metaplektičke grupe"

2017/2018

1. 28.05.2018., Sonja Žunar, PMF-MO, obrana doktorske disertacije, "Neponištavanja Poincaréovih redova na metaplektičkoj grupi i primjene"

19.05.2018. Workshop: On some recent developments in local and global representation theory.

2. 10:00-11:00 Allen Moy, The Hong Kong University of Science and Technology Title: Morita equivalence of Peter-Weyl Iwahori algebras Abstract: The Peter-Weyl idempotent of a parahoric subgroup is the sum of the idempotents of irreducible representations which have a nonzero Iwahori fixed vector. The associated convolution algebra is called a Peter-Weyl Iwahori algebra. We show any Peter-Weyl Iwahori algebra is Morita equivalent to the Iwahori-Hecke algebra. Both the Iwahori-Hecke algebra and a Peter-Weyl Iwahori algebra have a natural C*-algebra structure, and the Morita equivalence preserves irreducible hermitian and unitary modules. Both algebras have another anti-involution denoted as •, and the Morita equivalence preserves irreducible and unitary modules for the • involution. This work is joint with Dan Barbasch.

3. 11:15-12:15 Marko Tadić, PMF-MO Title: On unitarizability for classical p-adic groups Abstract: We shall discuss possibility of describing unitarizability of classical p-adic groups (in the case of any generalised rank) based only on the cuspidal reducibilities (i.e. reducibilities in the generalised rank one case), and explain how one can get this in the case of generalised rank three. We shall also comment the case of generic and spherical unitary duals of classical p-adic groups.

4. 14:00-15:00 Ivan Matić, Odjel za matematiku, Sveučilište u Osijeku Title: Reducibility and composition series of certain representations induced from the maximal parabolic subgroups Abstract: Let G_n denote either the group Sp(n, F) or SO(2n+1, F) over a non-archimedean local field F. We will discuss reducibility of certain representations of the group G_n which are obtained by the parabolic induction from the maximal parabolic subgroups, and may play an interesting role in the determination of the unitary dual. If time permits, in particular cases we will also discuss the composition series.

5. 15:15-16:15 Harald Grobner, Faculty of Mathematics, University of Vienna Title: Rationality and the refined global GGP-conjecture for definite unitary groups Abstract:The refined global GGP-conjecture states a very precise relationship between the global period integral of two cusp forms on unitary groups, on the one hand, and a quotient of special values of L-functions and local integrals, on the other hand. If the two cusp forms come from cuspidal automorphic representations, which are supercuspidal at one non-archimedean place, then this conjecture has been shown by Beuzard-Plessis — up to a sign. In this talk, we present a totally different approach to the refined GGP-conjecture for totally definite unitary groups via Whittaker-periods: As our major result we will prove the conjecture without the all-present assumption of local supercuspidality — up to certain algebraic numbers. (This is joint work with J. Lin.)

6. 16:30-16:45 Petar Bakić, PMF-MO Title: Theta lifts of generic representations Abstract: Using some recent results on theta lifts of tempered representations, we describe the theta correspondence for irreducible generic representations.

7. 16:45-17:00 Darija Brajković, Odjel za matematiku, Sveučilište u Osijeku Title: Representations of the p-adic group SO(7) Abstract: Examination of the structure of the non-unitary dual of the p-adic group SO(7) with the support on the minimal parabolic subgroup.

8. 17:00-17:15 Igor Ciganović, PMF-MO Title: Composition series of a class of standard representations Abstract: We decompose a class of standard representations built on cuspidal representation with one half cuspidal reducibility in terms of Moeglin Tadic classification of discrete series.

9. 17:15-17:30 Sonja Žunar, PMF-MO Title: Non-vanishing of Poincaré series on the metaplectic group Abstract: We will discuss a refinement of Muić's integral non-vanishing criterion for Poincaré series on unimodular locally compact Hausdorff groups and its applications to cusp forms of half-integral weight.

10. 17:30-17:45 Iva Kodrnja, Građevinski fakultet, Sveučilište u Zagrebu Title: Generic construction of models for modular curves Abstract: Using the bases of appropriate linear subspaces of the space of modular forms, we can find various projective models for associated modular curves.

---

11. 23.04.2018.,Petar Bakić, PMF-MO, "Theta liftovi generičkih reprezentacija II."
12. 16.04.2018.,Petar Bakić, PMF-MO, "Theta liftovi generičkih reprezentacija."
13. 15.01.2018.,Darija Brajković, Odjel za matematiku, Sveučilište u Osijeku, "Unitarni dual $p$-adske grupe $SO(7)$ s nosačem na minimalnoj paraboličkoj podgrupi"-obrana teme doktorske disertacije.
14. 11.12.2017.,Sonja Žunar, PMF-MO, "O analitičkom proširenju i neponištavanju L-funkcija II".
15. 04.12.2017.,Sonja Žunar, PMF-MO, "O analitičkom proširenju i neponištavanju L-funkcija".
16. 13.11.2017.,Sonja Žunar, PMF-MO, "O skalarnom produktu nekih kusp-formi polucijele težine".

2016/2017

1. 12.06.2017.,Sonja Žunar, PMF-MO, "O skalarnom produktu nekih automorfnih formi na grupi $Mp_2(\mathbf{R})$".
2. 22.05.2017.,Darija Brajković,Odjel za matematiku, Sveučilište u Osijeku, "Reprezentacije neparne specijalne ortogonalne grupe II."
3. 15.05.2017.,Darija Brajković,Odjel za matematiku, Sveučilište u Osijeku, "Reprezentacije neparne specijalne ortogonalne grupe."
4. 27.03.2017.,Ivan Matić,Odjel za matematiku, Sveučilište u Osijeku, "O reprezentacijama izomorfnim svom Aubert dualu."
5. 06.03.2017.,Sonja Žunar, PMF-MO, "Neponištavanje nekih Poincaréovih redova na metaplektičkoj grupi".
6. 13.02.2017., Petar Bakić, PMF-MO, "Theta liftovi temperiranih reprezentacija IV."
7. 06.02.2017., Petar Bakić, PMF-MO, "Theta liftovi temperiranih reprezentacija III."
8. 30.01.2017., Petar Bakić, PMF-MO, "Theta liftovi temperiranih reprezentacija II."
9. 23.01.2017., Petar Bakić, PMF-MO, "Theta liftovi temperiranih reprezentacija."
10. 16.01.2017., Allen Moy, Hong Kong University of Science and Technology, An Euler-Poincaré formula for a depth zero Bernstein projector. Abstract Work of Bezrukavnikov-Kazhdan-Varshavsky uses an equivariant system of trivial idempotents of Moy-Prasad groups to obtain an Euler-Poincaré formula for the r-depth Bernstein projector. We establish an Euler-Poincaré formula for the projector to an individual depth zero Bernstein component in terms of an equivariant system of Peter-Weyl idempotents of parahoric subgroups P associated to a block of the reductive quotient P. This work is joint with Dan Barbasch and Dan Ciubotaru.
11. 19.12.2016. Sonja Žunar, PMF-MO, Integrabilne reprezentacije grupe $Mp_2(\mathbf{R})$ i Poincaréovi redovi II.
12. 12.12.2016. Ivan Matić, Odjel za matematiku, Sveučilište u Osijeku, O eksplicitnom određivanju Aubert duala II.
13. 05.12.2016. Ivan Matić, Odjel za matematiku, Sveučilište u Osijeku, O eksplicitnom određivanju Aubert duala.
14. 14.11.2016. Sonja Žunar, PMF-MO, Integrabilne reprezentacije grupe $Mp_2(\mathbf{R})$ i Poincaréovi redovi.

2015/2016

1. 08.07.2016, Iva Kodrnja, Građevinski fakultet, obrana doktorske disertacije Modeli modularnih krivulja, modularne forme i eta-kvocijenti.
2. 04.07.2016, Petar Bakić, PMF-MO, obrana teme doktorske disertacije Theta liftovi ireducibilnih reprezentacija metaplektičke grupe
3. 27.06.2016, Petar Bakić, PMF-MO O theta korespondenciji II
4. 13.06.2016, Sonja Žunar, PMF-MO, javna obrana teme doktorske disertacije: Neponištavanja Poincaréovih redova na metaplektičkoj grupi i primjene
5. 25.04.2016, Petar Bakić, PMF-MO, O theta korespodenciji
6. 04.04.2016, Sonja Žunar, PMF-MO, Osnovna serija reprezentacija grupe $Mp_2(\mathbb{R})$
7. 21.03.2016, Iva Kodrnja, Građevinski fakultet, Eta kvocijenti III.
8. 14.03.2016, Iva Kodrnja, Građevinski fakultet, Eta kvocijenti II.
9. 16.02.2016., Sonja Žunar, PMF-MO, Dizanje modularnih formi do automorfnih formi u slučaju polucijele težine II.
10. 08.02.2016., Sonja Žunar, PMF-MO, Dizanje modularnih formi do automorfnih formi u slučaju polucijele težine .
11. 25.01.2016, Nevena Jurčević-Peček, Sveučilište u Rijeci, Teorija reprezentacija hermitskih kvaternionskih grupa nad $p$-adskim poljima (obrana doktorske disertacije).
12. 14.12.2015, Iva Kodrnja, Građevinski fakultet, Eta kvocijenti.
13. 07.12.2015, Ivan Krijan, PMF-MO, Sferičke reprezentacije grupe $GL_2$ nad $p$-adskim poljem IV.
14. 30.11.2015, Ivan Krijan, PMF-MO, Sferičke reprezentacije grupe $GL_2$ nad $p$-adskim poljem III.
15. 09.11.2015, Ivan Krijan, PMF-MO, Sferičke reprezentacije grupe $GL_2$ nad $p$-adskim poljem II.
16. 02.11.2015, Ivan Krijan, PMF-MO, Sferičke reprezentacije grupe $GL_2$ nad $p$-adskim poljem.

2014/2015

1. 07.09.2015, Nevena Jurčević Peček, Odjel za matematiku, Sveučilište u Rijeci, Teorija reprezentacija hermitskih kvaternionskih grupa nad p-adskim poljima.
2. 17.07. 2015. Yeansu Kim, Iowa State University, Applications of Tadić's structure formula. Abstract We will mainly explain the applications of Tadić's structure formula. Tadić's structure formula explicitly describe the Jacquet modules of induced representa- tions. One application is the classification of strongly positive representations of $GSpin$ groups. It has an application on the proof of the equality of L-functions through local Langlands correspondence in the case of $GSpin$ groups. That equality also has an interesting application in proving the generic Arthur L-packet conjec- ture. The generic Arthur L-packet conjecture states that if the L-packet attached to Arthur parameter has a generic member, then it is tempered. If time permits, I will explain the case of classical groups as well.
3. 15.06.2015. Iva Kodrnja, Građevinski fakultet, obrane teme doktorskog rada: Modeli modularnih krivulja, modularne forme i eta-kvocijenti.
4. 08.06.2015., Matias Victor Moya Giusti, Universit\'{e} Paris Diderot (Paris 7), On the existence of ghost classes in the cohomology of certain Shimura varieties,
   Abstract We begin by introducing the concept of ghost classes in the cohomology of locally symmetric spaces to fix some notations, then we explain a method to study the existence of ghost classes in the case of a Shimura variety of Q-rank 2, where the complex structure allows us to use the theory of Hodge structures. Finally we apply these strategies to the Shimura varieties associated to $GSp_4$ and $GU(2, 2).$
5. 04.05.2015., Sonja Žunar, Ireducibilne unitarne reprezentacije grupe $SL(2,\mathbb{R})$, dio II
6. 13.04.2015., Sonja Žunar, Ireducibilne unitarne reprezentacije grupe $SL(2,\mathbb{R})$, dio I
7. 23.03.2015., Petar Bakić, Reprezentacije grupe $GL(2)$ nad lokalnim nearhimedskim poljem - dio III
8. 16.03.2015., Petar Bakić, Reprezentacije grupe $GL(2)$ nad lokalnim nearhimedskim poljem - dio II
9. 09.03.2015., Petar Bakić, Reprezentacije grupe $GL(2)$ nad lokalnim nearhimedskim poljem - dio I
10. 19.01.2015, Jing Feng Lau, University of Singapore, On the residual spectrum of a quasi-split group of type D4
    Abstract In this talk, I will present the results for the residual spectrum of a quasi-split group of type D4 supported on maximal parabolics and some partial results for the residual spectrum supported on the Borel subgroup if time permits. This is work still in progress.
    
11. 01.12.2014, Nevena Jurčević, Matematički odjel, Sveučilište u Rijeci, Parabolička indukcija za klasične p-adske grupe.
12. 24.11.2014., Ivan Krijan, Reprezentacije kompaktnih grupa i Peter-Weylov teorem.
13. 27.10.2014., Sonja Žunar, Uvod u modularne forme.
14. 20.10.2014., Petar Bakić, Uvod u geometriju shema.

2013/2014

1. 01.09.2014., Shunsuke Yamana, Department of Mathematical Sciences, Kyushu University, Japan, Symmetric square L-functions for GL(n) and invariant trilinear forms,
   Abstract Following Bump-Ginzburg and Takeda, we develop a theory of symmetric square L-functions for GL(n). >We characterize its pole in terms of certain trilinear period integrals, determine all irreducible summands of the discrete spectrum of GL(n) having nonvanishing trilinear periods, and construct nonzero local invariant trilinear forms on a certain family of local induced representations.
   
2. 04.09.2014., Shunsuke Yamana, Department of Mathematical Sciences, Kyushu University, Japan, L-functions and theta correspondence,
   Abstract The doubling method of Piatetski-Shapiro and Rallis applies in the local situation to define local factors of representations of classical groups. On the one hand, the L-factor is defined as a g.c.d. of the local zeta integrals for all good sections. On the other hand, it is defined from the gamma factor by using the Langlands classification. In this talk I develop a theory of the zeta integral and prove that the two candidates of the L-factor agree. Applications include a characterization of nonvanishing of global theta liftings in terms of the analytic properties of the complete L-functions and the occurrence in the local theta correspondence.
3. 30.06.2014., Igor Ciganović, PMF-MO, Obrana doktorske disertacije
4. 16-20.06.2014.Representations of p-adic groups; A conference dedicated to Marko Tadić on his 60th birthday
5. 07.04.2014., Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa VII.
6. 24.03.2014., Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa VI.
7. 10.02.2014., Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa V.
8. 03.02.2014, Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa IV.
9. 16.12.2013, Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa III.
10. 09.12.2013, Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa II.
11. 02.12.2013, Iva Kodrnja, Građevinski fakultet, Geometrija Fuchsovih grupa.
12. 18.11.2013, Igor Ciganović, PMF-MO, Nerazgranate reprezentacije metaplekticke grupe.
13. 14.10.2013., Gordan Savin, University of Utah: Twisted Bhargava Cubes.

2012/2013

1. 01.07.2013., Dubravka Ban, Department of Mathematics, Southern Illinois University, Carbondale: $R$-grupe za $GSpin$ grupe.
2. 20.05.2013., Harald Grobner, University of Vienna, Periods and special values of automorphic L-functions
   Abstract In this talk we are going to present some recent results, obtained in joint work with M. Harris, on the algebraicity of special values of the Rankin-Selberg L-function and the adjoint L-function. The main methods will be automorphic cohomology and base change from unitary groups. We will also point out, how these results can be used, in order to show potential new results on the internal nature of cohomological and motivic periods.
3. 06.05.2013., Erez Lapid,Institute of Mathematics, Hebrew University of Jerusalem, Some analytic aspects of the trace formula.
   Abstract: in order to obtain applications of the trace formula in the spirit of Selberg one has to confront several analytic difficulties, both global and local. I will discuss what is known and remains to be done, based on joint work with Tobias Finis and Werner Muller.
4. 22.04.2013., Ivan Krijan, PMF-MO, Multipliciteti presjeka ravninskih krivulja.
5. 15.04.2013., Damir Mikoč, Odjel za matematiku, Sveučilište u Rijeci, Gornja poluravnina i Fuchsove grupe.
6. 18.03.2013., Igor Ciganović, PMF-MO Ireducibilne nerazgranate reprezentacije za klasične p-adske grupe II
7. 11.03.2013., Igor Ciganović, PMF-MO Ireducibilne nerazgranate reprezentacije za klasične p-adske grupe.
8. 19.11.2012., Igor Ciganović, PMF-MO Klasifikacija Zelevinskog za reprezentacije metaplektičke grupe II
9. 29.10.2012., Igor Ciganović, PMF-MO Klasifikacija Zelevinskog za reprezentacije metaplektičke grupe
10. 22.10.2012., Igor Ciganović, PMF-MO Geometrijska lema za metaplektičku grupu
11. 15.10.2012., Igor Ciganović, PMF-MO Parabolička indukcija i Jacquetov funktor za metaplektičku grupu III
12. 01.10.2012., Igor Ciganović, PMF-MO Parabolička indukcija i Jacquetov funktor za metaplektičku grupu II
13. 24.09.2012., Igor Ciganović, PMF-MO Parabolička indukcija i Jacquetov funktor za metaplektičku grupu.

2011/2012

1. 04.06.2012., Allen Moy , HKUST Two shorter talks on cusp forms and one K-type representations.
   Abstract: This talk will in fact be two shorter talks. The first talk is about cusp forms on a p-adic Lie algebra and Lie group. It is joint work in progress with Fiona Murnaghan and Xuhua He on a conjecture about cusp forms supported on the topologically nilpotent set. The second mini talk is about one K-type representations. The latter are representations of the Weyl group which can be extended to hermitian representations of the graded Hecke algebra and they yield unitary representations of the p-adic group. Examples of these are the Speh representations. In joint work with Dan Ciubotaru, we have noticed that the Dirac operator for a one K-type representation is zero. This makes them very interesting examples.
2. 9.12.2011, 15:00 (104) Abhishek Saha (ETH, Zurich), Transfer of Siegel modular forms
   Abstract:I will describe recent joint work with Ameya Pitale and Ralf Schmidt about the non-generic Langlands transfer of full-level Siegel modular forms from $GSp(4)$ to $GL(4)$. The method is based on the converse theorem of Cogdell and Piatetski-Shapiro and an integral representation of Furusawa for L-functions on $GSp(4) \times GL(2)$.
3. 8.12.2011., 13:00 (109) Abhishek Saha (ETH, Zurich), Determination of modular forms by Fourier coefficients
   Abstract:It is an interesting question when a natural subset of the Fourier coefficients are sufficient to uniquely determine a modular form. I will describe recent work that investigates this question for classical holomorphic cusp forms of half-integral weight, and Siegel cusp forms of genus 2. These two apparently very different scenarios turn out to be closely related, and have important consequences for the L-functions and Bessel models related to Siegel cusp forms. In particular, an application to the case of Yoshida lifts leads to a simultaneous non-vanishing theorem for two Rankin-Selberg L-functions. Part of this is joint work with Ralf Schmidt.
4. 17.11.2011., (13:00, predavaona 104), Gergely Harcos, Alfred Renyi Insitute of Mathematics, Budapest, A hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions
5. 10.10.2011., Ivan Matić, Odjel za matematiku, Osijek, Princip očuvanja za diskretne serije metaplektičkih grupa II
6. 03.10.2011., Ivan Matić, Odjel za matematiku, Osijek, Princip očuvanja za diskretne serije metaplektičkih grupa
7. 26.09.2011., Marcela Hanzer, PMF-MO, Eksplicitna konstrukcija automorfnih reprezentacija simplektičke grupe s kvadratnim unipotentnim Arthurovim parametrom III
8. 19.09.2011., Marcela Hanzer, PMF-MO, Eksplicitna konstrukcija automorfnih reprezentacija simplektičke grupe s kvadratnim unipotentnim Arthurovim parametrom II
9. 12.09.2011., Marcela Hanzer, PMF-MO, Eksplicitna konstrukcija automorfnih reprezentacija simplektičke grupe s kvadratnim unipotentnim Arthurovim parametrom.

---

2010/2011

1. 04.07.2011., Dubravka Ban, Klasične R-grupe i Arthurove R-grupe
2. 06.06.2011., Dragan Miličić, Geometrija i unitarnost
3. 30.05.2011., Igor Ciganović, Algebarski pristup klasifikaciji Zelevinskog za klasične p-adske grupe III
4. 23.05.2011., Igor Ciganović, Algebarski pristup klasifikaciji Zelevinskog za klasične p-adske grupe II
5. 09.05.2011., Igor Ciganović, Algebarski pristup klasifikaciji Zelevinskog za klasične p-adske grupe
6. 02.05.2011., Nevena Jurčević Peček, Reprezentacije kompaktnih grupa II
7. 18.04.2011., Nevena Jurčević Peček, Reprezentacije kompaktnih grupa I
8. 11.04.2011. Igor Ciganović, Reprezentacije simplektičkih grupa nad p-adskim poljem III
9. 4.04.2011. Igor Ciganović, Reprezentacije simplektičkih grupa nad p-adskim poljem II
10. 28.03.2011. Igor Ciganović, Reprezentacije simplektičkih grupa nad p-adskim poljem
11. 28.02.2011. Ioan Badulescu (University of Montpellier), An application of the Zelevinsky involution
    Abstract: Moeglin and Waldspurger gave an algorithm for computing the Zelevinsky involution. I will show how to use this algorithm to solve several problems concerning p-adic Speh representations (for example to show that Speh representations are unitary).
12. 20.12. 2010. G. Savin, Konstrukcija lokalnih polja u rezidualnoj karakteristici 2
13. 13.12. 2010. I. Matić, Jacquetovi moduli strogo pozitivnih diskretnih serija
14. 6.12. 2010. I. Matić, Strogo pozitivne reprezentacije metaplektičkih grupa
15. 22.11. 2010. G. Muić, Skalarni produkt automorfnih formi i primjene II
16. 15.11. 2010. G. Muić, Skalarni produkt automorfnih formi i primjene
17. 8.11.2010. I. Ciganović, Sfericke reprezentacije grupe $GL_2$ nad p-adskim poljem
18. 25.10.2010. N. Grbac, Automorfna kohomologija grupe $GL_2$ nad kvaternionskom algebrom
19. 4. 10.2010. I. Ciganović, Reprezentacije osnovne serije grupe $GL_2$ nad p-adskim poljem III
20. 27.09.2010. I. Ciganović, Reprezentacije osnovne serije grupe $GL_2$ nad p-adskim poljem II
21. 13.09.2010. I. Ciganović, Reprezentacije osnovne serije grupe $GL_2$ nad p-adskim poljem.

---

2009/2010

1. 15.3. 2010 M. Hanzer, Dualni unitarni reduktivni parovi i odnos reducibilnosti odgovarajućih induciranih reprezentacija II
2. 8.3. 2010 M. Hanzer, Dualni unitarni reduktivni parovi i odnos reducibilnosti odgovarajućih induciranih reprezentacija
3. 4.2. 2010 u 16:00 (predavaonica 108) I. Matić, obrana doktorske disertacije.
4. 18. 01. N. Grbac, Automorfna kohomologija reduktivnih grupa - nužni uvjeti neponištavanja 2
5. 11. 01. N. Grbac, Automorfna kohomologija reduktivnih grupa - nužni uvjeti neponištavanja
6. 21.12. N. Grbac, Automorfna kohomologija reduktivne grupe - Frankeova filtracija
7. 14.12. (ponedjeljak) u 16:15 G. Muić, Geometrijska gustoća Heckeovih karaktera i posljedice na strukturu kuspidalnog spektra poluproste algebarske grupe
8. 7.12. 2008. (s početkom u 16:15) I. Ciganović, Reprezentacije kompaktnih grupa
9. 30.11. 2008. (s početkom u 16:30) G. Muić, Sistem izvodnica za prostore kuspidalnih modularnih formi II
10. 23.11. 2008. (s početkom u 16:00) G. Muić, Sistem izvodnica za prostore kuspidalnih modularnih formi
11. 16. 11. 2009. A. Moy, Distribution algebras on a p-adic group and Lie algebra
12. 9.11. 2009. G. Muić, Nove konstrukcije i tehnike neponištavanja modularnih formi težine $>2$
13. 28. 09. 2009. A. Valent, Strogo pozitivne kvadratno--integrabilne reprezentacije grupe $GSp(n)$ I
14. 5. 10. 2009. A. Valent, Strogo pozitivne kvadratno--integrabilne reprezentacije grupe $GSp(n)$ II
15. 19.10. 2009. A. Valent, Kvadratno--integrabilne reprezentacije grupe $GSp(n)$

---

2008/2009

1. 25. 9. 2008. I.Matić, Struktura spinornih grupa
2. 15.12. 2008. I. Matić, Levijevi faktori p-adskog $Spin(2n+1)$
3. 22.12. 2008. s početkom u 11:30 u predavaonici 108 G. Muić, Egzistencija nekih tipova kuspidalnih automorfnih reprezentacija
4. 9. 3. M. Hanzer, Rang jedan reducibilnosti za metaplektičke grupe preko theta korespondencije
5. 16. 3. M. Hanzer, Rang jedan reducibilnosti za metaplektičke grupe preko theta korespondencije II
6. 23. 3. Igor Ciganović, Tateova konstrukcija L-funkcija pridruženih Hecke-ovim karakterima I
7. 30. 3. Igor Ciganović, Tateova konstrukcija L-funkcija pridruženih Hecke-ovim karakterima II
8. 7. 4. Igor Ciganović, Tateova konstrukcija L-funkcija pridruženih Hecke-ovim karakterima III
9. 27.4. N. Grbac: Eisensteinova kohomologija aritmetičkih podgrupa klasičnih grupa
10. 11.5. N. Grbac: Eisensteinova kohomologija aritmetičkih podgrupa klasičnih grupa II
11. 18.5. M. Hanzer: Unitarni dual dvolisnog natkrivača $Sp(4)$
12. 25.5. M. Hanzer: Unitarni dual dvolisnog natkrivača $Sp(4)$ II
13. 1.6. I. Ciganović, Heckeov dokaz funkcionalne jednadžbe za zeta funkcije I
14. 8. 6. I. Ciganović, Heckeov dokaz funkcionalne jednadžbe za zeta funkcije II
15. 7.7. 2009. u 18:00 Jeffrey Adler: Towards a lifting of representations of finite reductive groups

2007/2008

1. 6.11. 2007. I.Matić, Whittakerovi funkcionali
2. 13.11. 2007. A. Moy (Hong-Kong), Distribution algebras and the Bernstein center.
3. 20.11. 2007. I.Matić, Whittakerovi funkcionali II
4. 27.11. M. Hanzer, Unitarizabilnost jedne klase Aubert duala kvadratno--integrabilnih reprezentacija
5. (zajednički sa Seminar za teoriju brojeva i algebru) 28.11. 12:00 (točno)-13:00, predavaonica 001, Wayne Raskind (University of Southern California, Los Angeles), Totally degenerate reduction and the conjectures of Hodge and Tate
6. 18.12. M. Hanzer, Unitarizabilnost jedne klase Aubert duala kvadratno--integrabilnih reprezentacija II
7. 15. 1. 2008. G. Muić, Konstrukcija kuspidalnih automorfnih formi koristeći Poincarove redove I
8. 22. 1. 2008. G. Muić, Konstrukcija kuspidalnih automorfnih formi koristeći Poincarove redove II
9. 12.2. 2008. G. Savin (University of Utah), Rank one reducibility for $SO_{2n+1}$ and $Sp_{2n}$
10. 11.3. 2008. Ivan Matić, "Unitarni dual p-adskog $SO(5)$ I"
11. 18.3. 2008. Ivan Matić, "Unitarni dual p-adskog $SO(5)$ II"
12. 25.3. 2008. Ivan Matić, "Unitarni dual p-adskog $SO(5)$ III"
13. 8.4. 2008. Ivan Matić, "Unitarni dual p-adskog $SO(5)$ IV"
14. 15. 4. 2008. Davor Dragičević "Modularne forme polucijelog nivoa"
15. 21. 4. 2008. Neven Grbac "Posljedice Arthurovih slutnji na samodualne kuspidalne automorfne reprezentacije opće linearne grupe"
16. 29. 4. 2008. Davor Dragičević "Modularne forme polucijelog nivoa II"
17. 6.5. 2008. T. Oda (Tokyo University) "Realizations of discrete series representations of "small" semisimple Lie groups of higher rank"
18. 13. 5. Goran Muić "Automorfne realizacije ireducibilnih reprezentacija grupe $SL_2(R)$"
19. 20. 5. 2008. Davor Dragičević "Neke primjene modularnih formi"
20. 10. 6. 2008. Dubravka Ban, "Kriterij kvadratne integrabilnosti za natkrivajuće grupe"