Matrix convex sets and real algebraic geometry

Code

J1-2453 (C) - included in ARIS records

Head

Period

9/1/2020 - 8/31/2023

Range in 2023

0.47 FTE

Science

Natural sciences and mathematics (8)

Reseacher status

Researcher (8)
Junior expert or technical associate (0)

Education

Doctor's degree (8)

Sex

Man (8)

Status

Employed at RO (1)
Employed at RO and RRD (6)
No data on employment in RO (1)

No. of publications

10–99 (5)
100–999 (3)

Projects / Programmes source: ARIS

source: ARIS

Matrix convex sets and real algebraic geometry

Research activity

Code	Science	Field	Subfield
1.01.04	Natural sciences and mathematics	Mathematics	Algebra

Code	Science	Field
1.01	Natural Sciences	Mathematics

Keywords

real algebraic geometry, matrix convexity, positive polynomials, sums of squares, moment problem, free analysis

Evaluation (rules)

source: COBISS

Evaluation of bibliographic research performance indicators according to ARIS methodology

Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases

source: WoS

source: Scopus

source: COBISS

Researchers (8)

no.	Code	Name and surname	Research area	Role	Period	No. of publicationsNo. of publications
1.	28255	PhD Kristijan Cafuta	Mathematics	Researcher	2020 - 2023	31
2.	50783	PhD Timotej Hrga	Computer intensive methods and applications	Researcher	2023	23
3.	29584	PhD Marko Kandić	Mathematics	Researcher	2020 - 2023	64
4.	22353	PhD Igor Klep	Mathematics	Head	2020 - 2023	310
5.	20268	PhD Primož Moravec	Mathematics	Researcher	2020 - 2023	215
6.	22649	PhD Janez Povh	Computer intensive methods and applications	Researcher	2020 - 2023	341
7.	28585	PhD Klemen Šivic	Mathematics	Researcher	2022 - 2023	49
8.	36360	PhD Aljaž Zalar	Mathematics	Researcher	2020 - 2023	55

Organisations (2)

no.	Code	Research organisation	City	Registration number	No. of publicationsNo. of publications
1.	1554	University of Ljubljana, Faculty of Mathematics and Physics	Ljubljana	1627007	34,085
2.	0101	Institute of Mathematics, Physics and Mechanics	Ljubljana	5055598000	20,223

Abstract

Convexity is a basic notion from geometry that is applied for solving problems across many sciences. In optimization, convexity leads to reliable and numerically tractable problems. Convex optimization is employed in control theory, communications and networks, signal processing, mechanical engineering, finance, optimal design in statistics, coding theory, etc. This proposal aims to determine classes of optimization problems which are effectively convex ones, even if they do not look like it. Advances in free analysis and real algebraic geometry are yielding exciting new approaches to this question, but there are still fundamental challenges ahead. This proposal intends to overcome these by using algebraic, geometric and analytic tools in a novel way. The project is designed modularly consisting of two strands, one focusing on free function theory, and the other on real algebraic geometry and positivity of noncommutative functions. We will also vigorously pursue applications of free analysis to related fields such as operator algebra and quantum information theory. Key for this will be advances in algorithms and their implementations which we intend to make available online to the wider scientific community.