# Stanisław Łojasiewicz

Stanisław Łojasiewicz (9 October 1926 – 14 November 2002) was a Polish mathematician.[1]

Stanisław Łojasiewicz
Born9 October 1926
Died14 November 2002 (aged 76)
Nationality Poland
Alma materJagiellonian University
Known forŁojasiewicz inequality, Łojasiewicz factorization lemma
Scientific career
FieldsMathematics
InstitutionsJagiellonian University

## Biography

At the end of the 1950s, he solved the problem of distribution division by analytic functions. Its solution opened the road to important results in the new theory of partial differential equations. The method established by Łojasiewicz led him to advance the theory of semianalytic sets, which opened an important chapter in modern analysis.[1]

## Commemoration

The Łojasiewicz Lectures[2] are a series of annual lectures in mathematics given at the Jagiellonian University in honour of Łojasiewicz.

Year Lecturer University Country Title
2010 Shing-Tung Yau Harvard University China / United States Coupled system of Hermitian metrics with Hermitian Yang-Mills system
2011 Richard S. Hamilton Columbia University United States The Ricci flow in lower dimensions
2012 Bernard Malgrange Université Henri Poincaré France Differential algebraic groups
2013 Neil Trudinger Australian National University Australia Optimal transportation in the 21st century
2014 Fernando Codá Marquez Princeton University Brazil / United States The min-max theory of minimal surfaces and applications
2015 Noga Alon Tel Aviv University Israel Signrank and its applications in combinatorics and complexity
2017 Artur Avila Instituto Nacional de Matemática Pura e Aplicada / Centre national de la recherche scientifique Brazil / France One-frequency Schrödinger operators and the almost reducibility conjecture
2018 Luis A. Caffarelli University of Texas at Austin Argentina / United States Some models of segregation

## References

1. ^ a b Pawłucki, Wieslaw (2003), "Stanisław Łojasiewicz (1926–2002)" (PDF), Roczniki Polskiego Towarzystwa Matematycznego, Ser. II: Wiadomości Matematyczne (in Polish), 39: 183–190.
2. ^ "Łojasiewicz Lecture - Institute of Mathematics of the Jagiellonian University". www.im.uj.edu.pl. Retrieved 2016-12-27.
List of Polish people

This is a partial list of notable Polish or Polish-speaking or -writing persons. Persons of partial Polish heritage have their respective ancestries credited.

Tadeusz Ważewski (24 September 1896 – 5 September 1972) was a Polish mathematician.

Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract, introduced by Karol Borsuk to the study of the solutions of differential equations.

Łojasiewicz inequality

In real algebraic geometry, the Łojasiewicz inequality, named after Stanisław Łojasiewicz, gives an upper bound for the distance of a point to the nearest zero of a given real analytic function. Specifically, let ƒ : U → R be a real analytic function on an open set U in Rn, and let Z be the zero locus of ƒ. Assume that Z is not empty. Then for any compact set K in U, there exist positive constants α and C such that, for all x in K

${\displaystyle \operatorname {dist} (x,Z)^{\alpha }\leq C|f(x)|.}$

Here α can be large.

The following form of this inequality is often seen in more analytic contexts: with the same assumptions on ƒ, for every p ∈ U there is a possibly smaller open neighborhood W of p and constants θ ∈ (0,1) and c > 0 such that

${\displaystyle |f(x)-f(p)|^{\theta }\leq c|\nabla f(x)|.}$

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