sažeci za ak. god. 2025./2026.

Obrisani Korisnik — Wed, 22 Apr 2026 09:28:54 GMT

Dual Integrable Representations - Introduction

We will present the theory of dual integrable representations, a special class of unitary representations on locally compact groups. Some fifteen years ago the notion and the theory were developed in the case of Abelian (LCA) groups. In recent collaboration with Ivana Slamić (University of Rijeka) the theory was extended to the general non-Abelian case.

Using mathematical modelling to estimate the probability of a major outbreak early in infectious disease epidemics

When a pathogen enters a new location, a central public health question is whether sustained local transmission will follow. The probability of a major outbreak (PMO) provides a quantitative measure of this risk. In this talk, I will present three complementary methods for estimating the PMO from disease incidence time series data early in an outbreak. The first approach is based on classical branching process results (Method 1: Analytic). The second approach involves PMO inference via repeated model simulation, computing the proportion of simulations that match the dataset and subsequently result in a major outbreak (Method 2: Trajectory matching). The third approach uses model simulations to train a supervised machine learning classifier to predict the PMO from observed data (Method 3: Machine learning). Using a renewal equation model, I will show that Methods 2 and 3 produce PMO estimates that align with Method 1's analytic predictions, given sufficient simulated training data. The number of simulations required to obtain accurate estimates using Methods 2 and 3 depends on the dataset length in a complex way. For longer time series, fewer simulations match the dataset, but it may already be clear whether sustained transmission is underway. Finally, I will show how under-reporting can be accounted for in all three approaches, improving their applicability to real-world surveillance data. The suite of methods that I will showcase in this talk offers a framework for assessing future risks early in outbreaks of a range of pathogens.

Stability of Hölder regularity and weighted functional inequalities

In this talk, we first introduce new forms of tails of jumping measures and weighted functional inequalities for general symmetric Dirichlet forms on metric measure spaces under general volume doubling condition. Our framework covers Dirichlet forms with singular jumping measures including ones corresponding to trace processes. Using the new weighted functional inequalities, we establish stable equivalent characterizations of Hölder regularity of parabolic functions for symmetric Dirichlet forms. As consequences of the main result, we can show Hölder-continuity of parabolic functions for a large class of symmetric Markov processes blowing up to infinity at the boundary of state spaces. This talk is mainly based on a joint work with Soobin Cho (University of Illinois, USA).

Abnormal boundary decay for stable operators

Assume $\alpha\in (0, 2)$ and $d\ge 2$. Let ${\cal L}^\alpha$ be the generator of a symmetric, but not necessarily isotropic, $\alpha$-stable process $X$ in $\mathbb{R}^d$ whose L\'evy density is comparable with that of an isotropic $\alpha$-stable process. In this talk, I will present some recent results on the boundary decay of non-negative harmonic functions of ${\cal L}^\alpha$ in an open set $D$ and the boundary decay of the heat kernel $p^D(t,x,y)$ of the part process $X^D$ of $X$ on $D$. Our main result is that the $C^{1, \rm Dini}$ regularity assumption on $D\subset \R^d$ is optimal for the standard boundary decay property for nonnegative ${\cal L}^\alpha$-harmonic functions in $D$, and for the standard boundary decay property of $p^D(t,x,y)$. We obtain this result by proving the following: (i) If $D$ is a $C^{1, \rm Dini}$ open set and $h$ is a nonnegative function which is ${\cal L}^\alpha$-harmonic in $D$ and vanishes near a portion of $\partial D$, then the rate at which $h(x)$ decays to 0 near that portion of $\partial D$ is ${\rm dist} (x, D^c)^{\alpha/2}$. (ii) If $D$ is a $C^{1, \rm Dini}$ open set, then, as $x\to \partial D$, the rate at which $p^D(t,x,y)$ tends to 0 is ${\rm dist} (x, D^c)^{\alpha/2}$. (iii) For any non-Dini modulus of continuity $\ell$, there exist non-$C^{1, \rm Dini}$ open sets $D$, with $\partial D$ locally being the graph of a $C^{1, \ell}$ function, such that the standard boundary decay properties above do not hold for $D$.

Neki novi rezultati Fourierove analize višeg reda

Fourierova analiza višeg reda je poopćenje klasične Fourierove analize u kojem su linearne faze zamijenjene polinomijalnim (ili sličnim) fazama. Središnji objekti proučavanja su norme ujednačenosti, definirane za funkcije na danoj abelovoj grupi G i označene s U^k za red k \in \mathbb{N}, a koje potječu iz Gowersovog dokaza Szemerédijevog teorema. Ukratko, U^k norma mjeri koliko je polinomijalne strukture stupnja k-1 sadržano u danoj funkciji. Jedan od središnjih problema aditivne kombinatorike je takozvano inverzno pitanje za norme ujednačenosti: u danoj grupi G i za danu vrijednost c>0, kako izgleda $f : G \to \mathbb{C}$, sa $\|f\|_{\infty} \leq 1$ i $\|f\|_{U^k} \geq c$?
U ovom predavanju ću predstaviti par novih rezultata koji se tiču norme U^4. Poznati rezultati bavili su se isključivo ekstremnim slučajevima za ambijentnu grupu G, a to su cikličke grupe i vektorski prostori, gde su postojale jasne prepreke za generalizaciju na opći slučaj. Glavni rezultat o kojem ću govoriti je inverzni teorem koji vrijedi u svim abelovim grupama reda relativno prostog sa 6, a koji pritom vrijedi s kvazipolinomijalnim ocjenama.

Markovljevi procesi s jezgrom skokova koja opada na granici

U ovom predavanju dat ću pregled nekih rezultata koji se odnose na Markovljeve procese skokova (odnosno singularne nelokalne operatore) s jezgrom koja iščezava na rubu glatkog podskupa Euklidskoga prostora. Usredotočit ću se na temelje teorije koji omogućuju dobivanje potrebnih ocjena. Dobiveni rezultati predstavljaju generalizaciju sličnih rezultata u slučaju poluprostora.

Muckenhouptove težine

Muckenhouptove težine igraju osnovnu ulogu u analizi Calderon-Zygmundovih singularnih integralnih operatora, uključujući i važan slučaj Hardy-Littlewoodovog maksimalnog operatora. Od posebne je važnosti i njihova veza s BMO prostorima i harmonijskim mjerama. Predstavit ćemo rezultate vezane uz dva osnovna pitanja. Prvo je vezano uz ponašanje ovih težina ovisno o različitim pokrivačima, ponajviše o Garnett-Jonesovom teoremu distance. Drugo je vezano uz proširenje ovih težina na slučaj funkcija koje imaju vrijednosti u skupu matrica. Rezultati su nastali u suradnji s profesorom Morten Nielsenom sa Sveučilišta u Aalborgu u Danskoj.

seminari u ak. god. 2025./2026.

Obrisani Korisnik — Wed, 22 Apr 2026 09:30:29 GMT

12.5.2026. :: Hrvoje Šikić (PMF)
- Dual Integrable Representations - Introduction
14.4.2026. :: Karla Bonic-Babic (Mathematical Institute, University of Oxford)
- Using mathematical modelling to estimate the probability of a major outbreak early in infectious disease epidemics
7.4.2026. :: Panki Kim (Seoul National University)
- Stability of Hölder regularity and weighted functional inequalities
31.3.2026. :: Renming Song (University of Illinois Urbana-Champaign)
- Abnormal boundary decay for stable operators
24.2.2026. :: Luka Milićević (Matematički institut SANU)
- Neki novi rezultati Fourierove analize višeg reda
25.11.2025.
- 16:15h :: Zoran Vondraček (PMF, SOIS-FT) :: Markovljevi procesi s jezgrom skokova koja opada na granici
- 17:00h :: Hrvoje Šikić (PMF) :: Muckenhouptove težine

PMF - Seminar za teoriju vjerojatnosti

sažeci za ak. god. 2025./2026.

seminari u ak. god. 2025./2026.