Mathematical Colloquium

 

PROGRAM


ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

                      


PROGRAM ZA DECEMBAR 2018.


UTORAK, 04.12.2018 u 10:30, Sala 2, SANU, Kneza Mihaila 35
Bernd Sturmfels, Max Planck Institute
VARIETIES OF SIGNATURE TENSORS
We discuss recent developments in computational algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family we obtain an algebraic variety with interesting properties.



UTORAK, 18.12.2018 u 15:30, Sala 2, SANU, Kneza Mihaila 35
Erika Berenice Roldan Roa, The Ohio State University
EVOLUTION OF THE HOMOLOGY AND RELATED GEOMETRIC PROPERTIES OF THE EDEN GROWTH MODEL
In this talk, we study the persistent homology and related geometric properties of the evolution in time of a discrete-time stochastic process defined on the 2-dimensional regular square lattice. This process corresponds to a cell growth model called the Eden Growth Model(EGM). It can be described as follows: start with the cell square of the 2-dimensional regular square lattice of the plane that contains the origin; then make the cell structure grow by adding one cell at each time uniformly random to the perimeter. We give a characterization of the possible change in the rank of the first homology group of this process (the ``number of holes''). Based on this result we have designed and implemented a new algorithm that computes the persistent homology associated to this stochastic process and that also keeps track of geometric features related to the homology. Also, we present obtained results of computational experiments performed with this algorithm, and we establish conjectures about the asymptotic behavior of the homology and other related geometric random variables. The EGM can be seen as a First Passage Percolation model after a proper time-scaling. This is the first time that tools and techniques from stochastic topology and topological data analysis are used to measure the evolution of the topology of the EGM and in general in FPP models.

PETAK, 21.12.2018 u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Vladimir Dragović, Matematički institut SANU; Univerzitet u Teksasu
BILIJARI UNUTAR KVADRIKA I EKSTREMALNI POLINOMI
Predstavićemo novi spoj dve klasične teorije, o integrabilnim bilijarima u d dimenzionom euklidskom prostoru i o ekstremalnim polinomima na d realnih intervala. Već u ravanskom slučaju dobijaju se novi rezultati o kaustikama Ponseleovih poligona i njihovim vezama sa Zolotarjovljevim i Ahiezerovim polinomima. Otkriva se takođe i veza sa diskriminantno-separabilnim polinomima, koje je predavač uveo pre više godina, razmatrajući integraciju čigre Kovaljevske i dvoznačne Buhštaber-Novikovljeve grupe. U proizvoljnoj dimenziji daje se potpuna klasifikacija periodičkih trajektorija, koja se zasniva na nedavno dobijenim kombinatorno-aritmetičkim svojstvima rotacionih brojeva. Prikazani rezultati su deo zajedničkog rada sa Milenom Radnović.
Zajednički sastanak sa Odeljenjem za mehaniku.

SREDA, 26.12.2018 u 18:00, Sala 301f, MI SANU, Kneza Mihaila 36
Milena Radnović, Matematički institut SANU; Univerztet u Sidneju
O ASIMPTOTICI REŠENJA PENLEVEOVIH JEDNAČINA
U ovom predavanju ćemo izložiti konstrukciju i geometrijski opis prostora početnih vrednosti za Penleveove jednačine. Zatim ćemo prikazati rezultate o asimptotskom ponašanju Penleveovih transcendenata u tom prostoru, kada nezavisna promenljiva teži beskonačnosti. Rezultati su dobijeni u zajedničkom istraživanju sa Nalini Joši.
Zajednički sastanak sa Odeljenjem za mehaniku.




Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.


Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU