Online differential geometry seminar  June 7, 10am 


The seminar on differential geometry will continue with this lecture:
June 7, 10am, online on MS Teams and the seminar room on the second floor
Join via this LINK.
Radek Suchanek (Masaryk University):
Some remarks on variational nature of MongeAmpère equations in dimension four
Abstract:
I will present a necessary condition for the local solvability of the strong inverse variational problem in the context of MongeAmpère partial differential equations and firstorder Lagrangians. In contrast with the previous talk by Marcus Dafinger, this condition is given by comparing differential forms on the first jet bundle and is valid only for the aforementioned PDEs. To illustrate how this approach can be applied, we will examine the linear KleinGordon equation, first and second heavenly equations of Plebanski, Grant equation, and Husain equation. I will also speak about the drawbacks of the method when trying to generalize it to a system of equations. 
Last Updated on Thursday, 03 June 2021 09:16 

Online differential geometry seminar  May 31, 10am 


The seminar on differential geometry will continue with this lecture:
May 31, 10am, online on MS Teams and the seminar room on the second floor
Join via this LINK.
Marcus Dafinger (University of Jena):
On formal calculus of variations, Cartan formula and Noether's theorem
Abstract:
We give an introductory talk on the formal calculus of variations. Concepts from differential geometry, like Liederivative, exterior derivative and Cartan formula will be related to first variation, Helmholtz map and a kind of related Cartan formula. With the help of these operations we then formulate Noether's theorem and present some results on the socalled Takens' problem. 
Last Updated on Monday, 31 May 2021 08:07 
Online algebra seminar  May 13th, 1pm 


We will continue online on Thursday, May 13th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Nathanael Arkor
Higherorder algebraic theories and relative monads
Abstract: There have traditionally been two ways to reason about universal algebraic structure categorically: via algebraic theories, and via monads. It is well known that the two are tightly related: in particular, there is a correspondence between algebraic theories and a class of monads on the category of sets.
Motivated by the study of simple type theories, Fiore and Mahmoud introduced secondorder algebraic theories, which extend classical (firstorder) algebraic theories by variablebinding operators, such as the existential quantifier ∃x of firstorder logic; the differential operators d/dx analysis; and the λabstraction operator of the untyped λcalculus. Fiore and Mahmoud estab lished a correspondence between secondorder algebraic theories and a secondorder equational logic, but did not pursue a general understanding of the categorical structure of secondorder algebraic theories. In particular, the possibility of a monad–theory correspondence for second order algebraic theories was left as an open question. In this talk, I will present a generalisation of algebraic theories to higherorder structure, in particular subsuming the secondorder algebraic theories of Fiore and Mahmoud, and describe a universal property of the category of nthorder algebraic theories. The central result is a correspondence between (n + 1)thorder algebraic theories and a class of relative monads on the category of nthorder algebraic theories, which extends to a monad correspondence subsuming that of the classical setting. Finally, I will discuss how the perspective lent by higherorder algebraic theories sheds new light on the classical monad–theory correspondence.
This is a report on joint work with Dylan McDermott. 
Last Updated on Wednesday, 12 May 2021 15:57 
Online differential geometry seminar  May 17, 10am 


The seminar on differential geometry will continue with this lecture:
May 17, 10am, online on MS Teams
Join via this LINK.
Radoslaw Kycia (Masaryk university):
CoPoincare lemma and applications to physics
Abstract:
I will outline the construction of the homotopy operator for codifferential defined on Riemannian manifolds. This notion can be used to solve, in a starshaped open subset, many equations of mathematical physics including Dirac, Maxwell and string theory problems. I will also present an intriguing correspondence between (co)homotopy operator and Clifford algebra. I will also discuss various incarnations of spinors that appear in the literature. The talk is based on the draft [2] and [1].
[1]Radoslaw Kycia, The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator, Results in Mathematics 75, 122 (2020) [2] Radoslaw Kycia, The Poincare lemma for codifferential, anticoexact forms, and applications to physics, arXiv: 2009.08542 [math.DG]

Last Updated on Wednesday, 12 May 2021 15:54 
Online algebra seminar  May 6th, 2pm 


We will continue online on Thursday, May 6th, the special time of 14.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Walter Tholen
Spaces vs Categories, Perfect Maps vs Discrete Cofibrations
Abstract: We consider perfect maps of topological spaces and discrete cofibrations of categories to guide us into Burroni's notions of Tcategory and Tfunctor. In that environment we establish a socalled comprehensive factorization system that entails the classical StreetWalters system, as well as the (antiperfect, perfect)system for continuous maps of Tychonoff spaces known since the 1960s. (Based on joint work with Leila Yeganeh) 
Last Updated on Tuesday, 04 May 2021 10:09 

