HiDEAs to work with
Letterio Gatto (Polytechnic University of Turin, Italy)
Abstract: HiDEA is the acronym of Higher Derivations on Exterior Algebra, a project I am currently working on together with many collaborators, such as O. Behzad & A. Nasrollah Nejad (Iran), L. Rowen & I. Scherbak (Israel), A. Contiero, P. Salehyan & R. Vidal Martins (Brasil), S. Amukugu, M. Mugochi & G. Marelli (Namibia). Originally introduced by Hasse & Schmidt (1937) to extend Taylor expansions of analytic functions and Wronskians in in the realm of positive characteristic commutative algebra, the notion of Higher Order derivations (Hasse-Schmidt derivation in the sequel) provides an extremely rich theory when applied to the super--commutative situation supplied by exterior algebras of free modules. The purpose of this talk is to advertise HiDEAs practise, focusing on its main tool, the so-called integration by parts formula. The latter shows how the theory is concerned with multilinear algebra (via an extension of the Cayley-Hamilton theorem for possible infinite dimensional vector spaces), with intersection theory of Grassmannians (Schubert Calculus via Pieri's & Giambelli's formula), with Representation Theory and Mathematical Physics, given the spontaneously arising of the vertex operators occurring in the boson-fermion correspondence from the so-called Schubert Derivations. The talk aims to be general, non specialistic and self--contained, requiring no more than basics in multilinear algebra (exterior algebras), elementary calculus (Taylor expansions) and a little routine combinatorics (formal power series, partitions, symmetric functions).
mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
Comments: https://us02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAGOON
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Series comments: Description: Research webinar series
The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.
LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).
Videos of the talks can be viewed here.
Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.
Organizers: | Severin Barmeier, Frank Neumann*, Sibylle Schroll* |
*contact for this listing |