**Institute of Mathematics and Center of Theoretical Physics (PAS)**

**together with the Chair of Mathematical Methods in Physics (UW)**

**
invite in the academic year 2014/15 students, PhD students, **

**and researchers of each age**

**to the seminar**

** GEOMETRICAL METHODS IN PHYSICS**

**Fundamental geometric ideas come from physics. Differential geometry is
the area in which physics intuitions take their form and where a precise
language is constructed, in which problems of physics can be discussed. Is the language used today fitting to the realm
of contemporary physics? **

**Our seminar is thought of firstly, as a place for discussions on
foundations and relationships between algebra, geometry and physics, and
secondly, as a place for presentation of recent developments and achievements
in these areas. We**** agree**** with ****Arnold’s opinion that;**** **

**MATHEMATICS IS THE PART OF PHYSICS WHERE EXPERIMENTS
ARE CHEAP **

**Main topics include:**

** 1)
Differential geometry and formalisms of mechanics and field theory**

·
**Formalisms of Lagrange
and Hamilton with constraints and
generalizations**

·
**Geometry of higher order theories **

·
**Supergeometry**** and graded differential geometry**

** 2)
Geometry of jet bundles and PDEs**

·
**Cartan**** distributions, prolongations, and symmetries**

·
**Homological methods for
PDEs and classical field theories**

** 3)
Geometry and dynamics of quantum systems**

·
**Geometry of quantum
states, entanglement, and teleportation**

·
**Quantum fields**

** 4) Geometric control theory and control of
quantum systems**

·
**Vector**** distributions**

·
**Optimal control in
optics, chemistry, and technique.**

*This seminar could be a source of
good ideas and topics for master and PhD theses. It offers also many
possibilities for an international cooperation (scientific trips and visits,
internships, etc.)***. **

**The seminar takes place in the Institute of
Mathematics (PAS), Śniadeckich Street 8, **

**room 106, on
Wednesdays, 2.15 pm - 4.00 pm.**

**YOU ARE CORDIALLY INVITED**

**Janusz****
Grabowski and Bronisław Jakubczyk
(IMPAN), Katarzyna
Grabowska and **

**Paweł Urbański (UW), Marek Kuś (CFT)**

**Information
about the seminar can also be found on the web pages ****http://www.fuw.edu.pl/KMMF/sem.wto.html****, **