Keynote Speakers

Title of the talk:  An alternative Fueter Theorem on octonions and Clifford algebras 

Abstract:  In this talk we propose an alternative generalization of the quaternionic Fueter Theorem that associates to any holomorphic function a single axially Fueter-regular function. Given any slice-regular function, we prove a decomposition with components in the kernel of the third order operator ∂¯∆, where ∂¯ is the Cauchy-Riemann operator and ∆ is the corresponding Laplacian on an hypercomplex subspace. This decomposition defines a real-linear map that associates to any slice-regular function a (m-1)/2-tuple of axially monogenic functions ∂¯∆-Fueter mapping. Here m+1 is the dimension of the space. We show that, differently from higher powers of the ∆ operator, the ∂¯∆-Fueter mapping has always a small kernel.

Short Bio, including current research interests

I am Associate Professor at University of Trento.

Education: Degree in Mathematics at University of Trento, 'Perfezionamento' at Scuola Normale Superiore di Pisa

Previous affiliations: University of Milan (1989-1998) and University of 'Milano Bicocca' (1998-2001)

Current research interests: Complex, quaternionic and Clifford analysis in one and several variables; Slice analysis in one and several variables.

Title of the talk:  Coherent state transforms and Clifford analysis

Abstract:  I will describe some extensions of the classical Segal-Bargman coherent state transform to the realm of Clifford analysis. For context, I will also describe the use of generalized coherent state transforms in geometric quantization.

This is work in collaboration with Pei Dang, Will Kirwin, José Mourão, and Tao Qian.

Short Bio, including current research interests

I am Associate Professor with Habilitation at Instituto Superior Técnico (IST) of the University of Lisbon and member of the Center for Mathematical Analysis, Geometry and Dynamical Systems at IST.

In recent years, I have been working in the field of geometric quantization. The general problem in this field is to understand the quantization of symplectic manifolds. Coherent state transforms, in generalized form, play an important role in this process: they relate different quantizations of a given symplectic manifold. They are also closely related to Hamiltonian flows in imaginary time in Kähler geometry.