We have scientific talks by RISC members or by invited renowned researchers on a regular basis in the RISC Colloquium, usually on Monday afternoon. From time to time our guests give talks also in one of the research seminars.

Past Talks

10/06/202413:30 - 14:30RISC Seminarroom, Castle of Hagenberg

A (soft) intro to quantum computing

Quantum computers are *not* the next generation of supercomputers. Rather, they are an attempt to rethink the way we load in, store and process information. The basic information carriers -- so called qubits -- are realized at the microscale. There, ...

24/05/202410:00 - 11:00HA 105 RISC Hagenberg and online via Zoom: Meeting ID: 973 8220 2890 Passwort: RISC

In this talk we present a summary of the articles contained in our Habilitation treatise. These articles are about algorithms related to proving identities and congruences linked to modular functions. Also we present theorems that are naturally connected to such ...

I invite all faculty and students at JKU and FH Hagenberg who are interested in the logical, semantical, and structural foundations of natural languages and algorithmic tools to do research in this area. Gérard Huet is one of the early ...

30/06/202214:00 - 16:00ONLY ONLINE via ZOOM! Meeting-ID: 945 0781 4483, Password: HaveFun

CHANGE OF THE LOCATION: Talk of Prof. Andrews “Separable Integer Partition Classes”

Abstract: Three of the most classical and well-known identities in the theory of partitions concern: (1) the generating function for p(n) (Euler); (2) the generating function for partitions into distinct parts (Euler), and (3) the generating function for partitions in ...

25/04/202213:30 - 14:30online via Zoom Meeting-ID: 949 1945 8950 Password: 135891

RISC Colloquium Talk: “Lucas congruences and congruence schemes”

It is a well-known and beautiful classical result of Lucas that, modulo a prime $p$, the binomial coefficients satisfy the congruences \begin{equation*} \binom{n}{k} \equiv \binom{n_0}{k_0} \binom{n_1}{k_1} \cdots \binom{n_r}{k_r}, \end{equation*} where $n_i$, respectively $k_i$, are the $p$-adic digits of $n$ and ...

23/03/202215:00 - 16:00Zoom-Login: Meeting-ID: 945 0781 4483 Password: HaveFun

Talk by Prof. Ono: “Sato-Tate type distributions for hypergeometric varieties”

Abstract: Studying the statistical behavior of number theoretic quantities is presently in vogue. This lecture will begin with a new look at classical results in number theory from the perspective of arithmetic statistics, which then naturally leads to point counts ...

30/06/202111:30 - 12:20online via Zoom

Symbolic Summation in Difference Rings and Challenging Applications

Application Presentation

ABSTRACT: My main research interest is computer algebra: I develop algorithmic theories in algebra, implement efficient and stable software packages based on these sophisticated theories, and apply them to non-trivial problems in mathematics and interdisciplinary research areas. In the first ...

30/06/202109:00 - 09:50online via Zoom

Symbolic Computation and Special Functions

Application Presentation

ABSTRACT: Special functions always had a central role in my research. Even though they are very classical objects, they haven't revealed all their secrets and new ways to apply them are constantly discovered. From the viewpoint of symbolic computation, they ...

29/06/202110:15 - 11:05online via Zoom

Torsion, Localization and Closure

Application Presentation

ABSTRACT: In algebra, localization is a systematic way to create bigger rings (up to the ring of fractions) from a given one by inverting some sets of ring's elements. Localization applies naturally to ideals and modules over these rings. In ...

29/06/202109:00 - 09:50online via Zoom

Solving symbolic constraints (approximately)

Application Presentation

ABSTRACT: Symbolic constraint solving is ubiquitous in many areas of mathematics and computer science. Unification, matching, anti-unification, disunification, and ordering constraints are some prominent examples that play an important role in automated reasoning, term rewriting, declarative programming, and their applications. ...

28/06/202115:00 - 15:50online via Zoom

Symbolic computation for ODEs with parameters

Application Presentation

ABSTRACT: Symbolic computation is useful in experimental design, in particular, in analyzing and improving ODE models with parameters. In this talk, we will consider one such application: the parameter identifiability problem. This problem is to decide whether the parameters of ...

ABSTRACT: Checking the satisfiability of quantifier-free real-arithmetic formulas is a practically highly relevant but computationally hard problem. Some beautiful mathematical decision procedures implemented in computer algebra systems are capable of solving such problems, however, they were developed for more general ...

28/06/202109:00 - 09:50online via Zoom

Symbolic computation through the holonomic looking-glass

Application Presentation

ABSTRACT: Symbolic computation is an evolving research area at the interplay between mathematics and computer science, which has found applications in nearly all fields of science. A branch of symbolic computation that has established particularly many such connections, is the ...

19/11/202010:15 - 11:45Zoom: Meeting-ID: 944 4280 2092 Passwort: 677177

Walks in the three-quarter plane

Enumeration of lattice walks in cones has many applications in combinatorics and probability theory. These objects are amenable to treatment by many techniques: combinatorics, complex analysis, probability theory, computer algebra and Galois theory of difference equations. While walks restricted to ...

05/11/202010:15 - 11:45Zoom: Meeting-ID: 944 4280 2092 Passwort: 677177

Topological rewriting systems applied to standard bases and syntactic algebras

We introduce topological rewriting systems as a generalisation of abstract rewriting systems, where we replace the set of terms by a topological space. Abstract rewriting systems correspond to topological rewriting systems for the discrete topology. We introduce the topological confluence ...

Semirings are a generalization of rings, where the subtraction is not available. They appear naturally in many branches of mathematics and informatics. In cryptograhy, simple semiring were suggested as suitable candidates for so called post-quantum cryptography, i.e. for protocols ...

A reflexive polytope is a lattice polytope whose dual polytope is again a lattice polytope. In my talk, after reviewing reflexive polytopes from a viewpoint of enumeration of lattice points, current topics related to the construction of reflexive polytopes by ...

The starting point of the talk is how to measure how big an infinite dimensional algebra is. In particular, we discuss the problem how to construct graded algebras with prescribed Hilbert series, including Hilbert series which are algebraic but not ...

In this talk I will explain a Connection between Commutative Algebra and Linear and Integer Programming. In the first part, it is explained how one can translate the Problem of bounding the index of stability of the Castelnuovo-Mumford regularities of ...

19/07/201810:15 - 11:30Seminarroom RISC Hagenberg

Radical Varieties

In many applications, where geometric constructions appear, parametrizations of the geometric objects are used. In practice, when the geometric entities are algebraic, the varieties are assumed to be rational, and hence representable by means of rational functions. This is a ...

30/05/201814:00 - 16:00RISC Seminar room

Truncated Hecke-Rogers type series

Prof. Ae Ya Yee

The recent work of George Andrews and Mircea Merca on the truncated version of Euler’s pentagonal number theorem has opened up a new study on truncated theta series. Since then several papers on the topic have followed. In collaboration with ...

18/05/201814:00 - 14:50RISC Seminar room


Prof. Adalbert Kerber
18/05/201810:40 - 11:30RISC Seminar room

Combinatorics on polynomial equations: do they describe nice varieties?

Prof. Joachim von zur Gathen

Combinatorics on polynomial equations: do they describe nice varieties? Joachim von zur Gathen Abstract: We consider natural combinatorial questions about systems of multivariate polynomials over a finite field and the variety V that they define over an algebraic closure. Fixing ...

18/05/201809:30 - 10:20RISC Seminar room

Chain Partition Analysis

Prof. Matthias Beck

Chain Partition Analysis Matthias Beck Abstract: We introduce and study a hybrid of (restricted) partition functions from combinatorial number theory and zeta polynomials from the theory of partially ordered sets (posets), giving rise to a concept that in a sense ...

17/05/201815:20 - 16:20RISC Seminar room

Eigenvalues, invariant factors and random integer matrices

Prof. Mark Giesbrecht

Integer matrices are often characterized by the lattice of combinations of their rows or columns. This is captured nicely by the Smith canonical form, a diagonal matrix of invariant factors, to which any integer matrix can be transformed through left ...

17/05/201814:00 - 15:00RISC Seminar room

Ramanujan’s Lost Notebook in Five Volumes__Reflections

Prof. George E. Andrews

Ramanujan's Lost Notebook in Five Volumes__Reflections George E. Andrews Abstract: Bruce Berndt and I have recently completed the fifth and final volume on Ramanujan's Lost Notebook. All of Ramanujan's assertions (with perhaps one of two exceptions) have been proved or, ...

17/05/201810:20 - 11:10RISC Seminar room

Some Hankel determinants with nice evaluations

Prof. Johann Cigler

Some Hankel determinants with nice evaluations Johann Cigler Abstract: We give some results and conjectures about Hankel determinants with nice evaluations: Hankel determinants of convolution powers of Catalan numbers Cn, different approaches to Hankel determinants of sequences such as (1, ...

27/11/201713:30 - 14:30RISC Seminar room

African research institute for Mathematics

Prof. Dr. Mama Foupouagnigni

AIMS is the main African research institute for Mathematics. The research area of the chairman Professor Foupouagniagni is computational mathematics, in particular symbolic computation and mathematical software. He will speak about the structure and the far-reaching goals of AIMS for ...

08/11/201714:00 - 15:30RISC Seminar room

Ramanujan’s Lost Notebook: History and Content

Prof. Bruce Berndt

In the spring of 1976, George Andrews discovered Ramanujan's "Lost Notebook" in the library of Trinity College, Cambridge. The "Lost Notebook" is not a notebook, but a sheaf of over 100 handwritten pages made by Ramanujan during the last year ...

06/11/201713:30 - 14:30RISC Seminar room

Ramanujan’s Life and Earlier Notebooks

Prof. Bruce Berndt

Generally regarded as India's greatest mathematician, Srinivasa Ramanujan was born in the southern Indian town of Kumbakonam on December 22, 1887 and died in Madras at the age of 32 in 1920. Before going to England in 1914 at the ...

31/10/201714:00 - 15:30RISC Seminar room

Walks, Difference Equations and Elliptic Curves

Prof. Michael Singer

In the recent years, the nature of the generating series of the walks in the quarter plane have attracted the attention of many authors. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least ...

30/10/201713:30 - 14:30RISC Seminar room

Groups and the Gamma Function

Prof. Michael Singer

In 1887, Hölder proved that the Gamma function, defined by the difference equation y(x+1) = x y(x), satisfies no nonzero polynomial differential equation with complex coefficients. In this talk I will describe a Galois theory that allows one to reprove ...

08/02/201714:00 - 16:00RISC Seminar room

4-Shadows in q-Series: Gupta, Kimberling, the Garden of Eden and the OEIS.

Prof. George Andrews

TALK ANNOUNCEMENT: Special RISC Algorithmic Combinatorics Seminar Abstract: This talk is devoted to discussing the implications of a very elementary technique for proving mod 4 congruences in the theory of partitions. It starts with a tribute to the late Hans ...

07/02/201711:00 - 12:00RISC Seminar room

The Man Who Knew Infinity: the Movie, the Man, and the Mathematics

Prof. George E. Andrews

*RISC Colloquium Announcement with corrected date* Abstract: In the spring of last year, the motion picture, The Man Who Knew Infinity, was released. It is now available on DVD. The movie tells the life story of the Indian genius, Ramanujan. ...

17/10/201615:00 - 16:30RISC Seminar room

A new approach to categorical semantics for procedural language

Dr. William Steingartner

The semantics of programs written in some languages is concerned with the interpretation in various types of models. We present a new approach to semantics: behavior of programs, i.e. changes of states is modeled in the category of states. ...

22/09/201614:30 - 16:00RISC Castle Seminar room

Approximate polynomial GCD by approximate syzygies, redux

Dr. Daniel Lichtblau

I will show in brief how one can compute the GCD of a pair of multivariate polynomials by finding a syzygy. I will then show how we can weaken this and create an "approximate syzygy" to find an approximate GCD. ...

09/05/201613:30 - 14:30RISC Seminar room

Linear Algebra 1.6

Prof. Martin Kreuzer

Most algebraists believe they know Linear Algebra. The purpose of this talk is to indicate that this is not necessarily true. We show a substantial amount of "new" Linear Algebra and its connection to Algebraic Geometry, in particular to the ...

03/05/201615:00 - 16:00RISC Seminar room

A new companion to Göllnitz’ (Big) partition theorem

Prof. Krishnaswami Alladi

Title: A new companion to Göllnitz' (Big) partition theorem Speaker: Professor Krishnaswami Alladi University of Florida, USA Time and Location: Tuesday, March 3, 2016 Seminar room castle, RISC, Hagenberg Abstract: One of the deepest results in the theory of partitions ...

25/04/201613:30 - 14:30RISC Seminar room

Paul Erdoes – one of the most influential mathematicians of our times

Prof. Krishnaswami Alladi

Note: This is a talk for a general audience and for students. Abstract: Paul Erdoes (1913-1996) was one of the most influential mathematicians of the twentieth century. 2013 was his 100-th birthday year. A Hungarian by birth, Erdoes had no ...

03/03/201614:00 - 16:00RISC Seminar room, pond

Twisting the quantum

Dr. Charles Clark

Title: Twisting the quantum Speaker: Prof. Charles W. Clark Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland College Park, Maryland, USA Time and Location: Thursday, March 3, 2016 2:00 pm, Seminar room pond, RISC, ...

22/01/201611:00 - 13:00RISC Seminar room

Twenty years of Lambert W

Prof. David Jeffrey

The year 2016 marks 20 years since the publication of the paper "On the Lambert W function". As will be pointed out, the function was studied before 1996, but this publication has proved to be the most cited reference. The ...

26/03/201514:00 - 16:00RISC Seminar room

Problems I cannot do – that people at RISC hopefully could do

Prof. Dennis Stanton

I will discuss open problems in enumeration, including partitions, and special functions. This will include the Rogers-Ramanujan identities, Gessel paths, the Omega operator, generalized super Catalan numbers, very well poised series, finite difference calculus, finite fields, and homology questions. ...

25/03/201514:00 - 16:00RISC Seminar room

Another (q,t)-world

Prof. Dennis Stanton

A well studied (q,t)-analogue of symmetric functions are the Macdonald polynomials. In this talk I will survey another (q,t)-analogue, where q is a prime power from a finite field and t is an indeterminate. Analogues of facts about ...

11/03/201514:00 - 16:00RISC Seminar room

Congruences for Fishburn Numbers

Prof. James Sellers

The Fishburn numbers, originally considered by Peter C. Fishburn, have been shown to enumerate a variety of combinatorial objects. These include unlabelled interval orders on n elements, (2+2)--avoiding posets with n elements, upper triangular matrices with nonnegative integer entries and ...

09/03/201513:30 - 14:30RISC Seminar room

Buchberger Theory for Effective Associative Rings

Prof. Teo Mora

The extension of Buchberger Theory and Algorithm from the classical case of polynomial rings over a field[1, 2, 3] to the case of (non necessarily commutative) monoid rings over a (non necessarily free) monoid and a principal ideal ring was ...

We propose a novel method to model real online social networks where our growing scale-free networks have tunable clustering coefficient. Models which based on purely preferential attachment are not able to describe high clustering coefficient of social networks. Beside the ...

13/11/201314:00 - 15:30RISC Seminar room pond

Entringer numbers and Poupard Calculus

Dominique Foata

Refinements of the celebrated tangent and secant numbers give rise to bivariate statistical distributions that can be expressed, either by a finite difference equation system, or by a three-variate exponential generating function. The underlying combinatorial sets, counted by tangent and ...

09/10/201314:00 - 16:00RISC Seminar room

On the ubiquity of modular forms and Apery-like numbers

Armin Straub

In the first part of this talk, we give examples from the theories of short random walks, binomial congruences, positivity of rational functions and series for $1/\pi$, in which modular forms and Apery-like numbers appear naturally (though not necessarily obviously). ...

28/06/201311:30 - 12:30RISC Seminar room pond

The Convex Hull of a Space Curve

Bernd Sturmfels

The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and stationary bisecants. We express the degree of this ...

24/06/201313:30 - 14:30RISC Seminar room

Teaching Semantics with a Proof Assistant or No more LSD trip proofs

Tobias Nipkow

The gulf between many computer science students and rigorous proofs is well known and much lamented. Teachers are frequently confronted with student ``proofs'' that look more like LSD trips than coherent chains of logic. In this talk I will present ...

06/03/201314:00 - 16:00RISC Seminar room

Old and New Results for Generalized Frobenius Partition Functions

James Sellers

In his 1984 AMS Memoir, George Andrews defined two families of generalized Frobenius partition functions which he denoted $\phi_k(n)$ and $c\phi_k(n)$ where $k\geq 1.$ Both of these functions "naturally" generalize the unrestricted partition function $p(n)$ since $p(n) = \phi_1(n) ...

09/01/201314:00 - 15:30RISC Seminar room

A unified method to prove Rogers-Ramanujan generalizations

Kagan Kursungöz

The first of the famous Rogers-Ramanujan identities states that the number of partitions of a positive integer n into distinct non-consecutive parts equals the number of partitions of n into parts that are 1 or 4 mod 5. Gordon later ...

05/12/201214:00 - 16:00RISC Seminar room

Rogue waves: A linear approximation

Sergei Suslov

ROGUE WAVES: A LINEAR APPROXIMATION Sergei K. Suslov School of Mathematical and Statistical Sciences, Arizona State University Abstract We elaborate on the phenomenon of Giant, Freak, or Rogue Waves in the ocean. A simplest possible explanation, in a linear approximation, ...

17/10/201214:00 - 16:00RISC Seminar room

Modularity of Kac Wakimoto characters

Kathrin Bringmann

In joint work with Amanda Folsom, we resolve a question of Kac, and explain the automorphic properties of certain characters due to Kac and Wakimoto. We prove that they are essentially holomorphic parts of certain generalizations of harmonic weak Maass ...

15/10/201213:30 - 14:30RISC Seminar room

Improvements and Extensions to CAD-Based Quantifier Elimination

Scott McCallum

The talk will informally describe some relatively recent improvements and extensions to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE). The improvements include improved projection operators and the use of equational constraints (where present) to further reduce the size of ...

24/09/201213:30 - 14:30RISC Seminar room

Classical modular polynomials over GF(2)

Petr Lisonek

For a prime number l, the classical modular polynomial Phi_l (sometimes called the modular equation of level l) is a polynomial with integer coefficients such that Phi_l(j(t),j(lt))=0 where j(t) is the j-invariant well known from the theory of elliptic ...

16/07/201213:30 - 14:30RISC Seminar room

Set theoretical aspects of Game Theory

Samuel Cristobal Centenera

At the beginning mathematics enabled a systematic approach to popular games giving advantage to the perceptive player, however nowadays it is also common to reformulate conjectures and theorems in term of games, in a way that if one were able ...

20/06/201212:30 - 13:15RISC Seminar room

A generalized queueing network model to study Proxy Cache Servers

Tamas Berczes

In this talk we treat a modification of the performance model of Proxy Cache Servers to a more powerful case when the inter-arrival times and the service times are generally distributed. First we describe the original Proxy Cache Server model ...

04/06/201213:30 - 14:30RISC Seminar room

Algebraic& Statistic Computation for Model Checking in BioInformatics

Quoc-Nam Tran

Temporal model checking is an algorithmic and formal approach for automatically verifying whether a finite-state concurrent system such as a sequential circuit design functions correctly. Typically, computation is carried over Boolean algebras using binary decision diagrams (BDDs) or satisfiability (SAT) ...

28/03/201214:00 - 00:00RISC Seminar room

Integer Partitions from a Geometric Viewpoint

Matthias Beck

The study of partitions and compositions (i.e., ordered partitions) of integers goes back centuries and has applications in various areas within and outside of mathematics. Partition analysis is full of beautiful--and sometimes surprising--identities, starting with Euler's classic theorem ...

28/03/201214:00 - 16:00RISC Seminar room

Integer Partitions from a Geometric Viewpoint

Matthias Beck

The study of partitions and compositions (i.e., ordered partitions) of integers goes back centuries and has applications in various areas within and outside of mathematics. Partition analysis is full of beautiful--and sometimes surprising--identities, starting with Euler's classic theorem ...

26/03/201213:30 - 14:30RISC Seminar room

Integer-point Enumeration in Polyhedra

Matthias Beck

We use generating functions and complex-analytic methods to count integer lattice points in polytopes with rational vertices. More precisely, we study the number of lattice points as the polytope gets dilated by an integer factor. This expression is known as ...

23/01/201213:30 - 14:30RISC Seminar room

Branch cuts – not just a technical detail

James Davenport

The precise definition of functions such as inverse sine is generally thought of as a tedious business, settled by Abramowitz and Stegun. However, the concept of branch cuts, and more generally the fact that functions such as sine do not ...