Summer School on

“An Interdisciplinary Approach to Tensor Decomposition”

Trento, July 14-18, 2014

Program

	Monday, 14	Tuesday, 15	Wednesday, 16	Thursday, 17	Friday, 18
9:00-9:30	Registration	LANDSBERG	RANESTAD	MOURRAIN	Working session
9:30-10:30	LANDSBERG	LANDSBERG	RANESTAD	MOURRAIN	Working session
10:30-11:00	Coffee break	Coffee break	Coffee break	Coffee break	Coffee break
11:00-12:00	MOURRAIN	MOURRAIN	LANDSBERG	RANESTAD	BOCCI
12:00-12:30	RANESTAD	MOURRAIN	LANDSBERG	RANESTAD
12:30-13:00	RANESTAD				Lunch
13:00	Lunch	Lunch	Lunch	Lunch
14:30-15:00					DOMANOV
15:00-15:30	EGGERMONT	BRAMBILLA	Free afternoon	Working session	POKORA
15:30-16:00	IKENMEYER	BRAMBILLA		Working session	SZPOND
16:00-16:30	MICHALEK	Coffee break		Working session	Coffee break
16:30-17:00	Coffee break	Working session		Coffee break	VILLAMIZAR
17:00-17:30	ANGELINI	Working session		CARLINI	BUCZYNSKI
17:30-18:00	HOROBET	Working session		CARLINI	ONETO
20:30				Social dinner

Monday, July 14^th

9:00-9:30 Registration

9:30-10:30 Joseph M. Landsberg: Tensor decomposition: motivations from applications, Espig
et. al. definition of “format”

10:30-11:00 Coffee break

11:00-12:00 Bernard Mourrain: 1. Sparse modeling from moments (sum of exponentials, Prony’s
method, duality)

12:00-13:00 Kristian Ranestad: Apolarity, rank versus cactus rank, examples: binary forms and
monomials

13:00 Lunch

15:00-15:30 Rob Eggermont: Plücker varieties

15:30-16:00 Christian Ikenmeyer: 16051 formulas for Ottaviani’s invariant of cubic threefolds

16:00-16:30 Mateusz Michalek: Cumulant approach to low rank tensors

16:30-17:00 Coffee break

17:00-17:30 Elena Angelini: Logarithmic bundles of multi-degree arrangements in P^n

17:30-18:00 Emil Horobet: The average number of critical rank-one approximations to a tensor

Tuesday, July 15^th

9:00-10:30 Joseph M. Landsberg: Equations for decompositions: Sylvester, flattenings,
Aronhold/Barth/Strassen/Toeplitz equations, Koszul flattenings, Hilbert flattenings

10:30-11:00 Coffee break

11:00-12:30 Bernard Mourrain: 2. Artinian algebra defined by linear form (structure, operators
of multiplication, Gorenstein algebra, positive linear forms)

3. Flat extension and decomposition algorithm (rank, commutation, orthogonal
polynomials, generalized Prony’s method)

13:00 Lunch

15:00-16:00 Maria Chiara Brambilla: Tensors, secant varieties and interpolation problems

16:00-16:30 Coffee break

16:30-18:00 Working session

Wednesday, July 16^th

9:00-10:30 Kristian Ranestad: Artinian Gorenstein rings, Hilbert function and hidden variables.
Local cactus rank, the cubic surface case

10:30-11:00 Coffee break

11:00-12:30 Joseph M. Landsberg: Rank v. border rank: Exploiting equations that give lower
bounds on border rank to get further lower bounds on rank

13:00 Lunch

Free afternoon

Thursday, July 17^th

9:00-10:30 Bernard Mourrain: 4. Tensor decomposition problem (apolarity, extension property,
examples)

5: Equations and Hilbert scheme (apolar ideals, generalized additive decomposition, geometric point of view)

10:30-11:00 Coffee break

11:00-12:30 Kristian Ranestad: Varieties of apolar subschemes, ternary case. Further examples,
and open problems

13:00 Lunch

15:00-16:30 Working session

16:30-17:00 Coffee break

17:00-18:00 Enrico Carlini: Symmetric tensors and apolarity

20:30 Social dinner

Friday, July 18^th

9:00-10:30 Working session

10:30-11:00 Coffee break

11:00-12:00 Cristiano Bocci: Identifiability of Segre products

12:30 Lunch

14:30-15:00 Ignat Domanov: Canonical polyadic decomposition of third-order tensors:
uniqueness and algebraic algorithms

15:00-15:30 Piotr Pokora: Symbolic powers of ideals versus Bounded Negativity Conjecture

15:30-16:00 Justyna Szpond: Symbolic generic initial systems of star configurations

16:00-16:30 Coffee break

16:30-17:00 Nelly Villamizar: Fat points ideals and the dimension problem of spline spaces

17:00-17:30 Jaroslaw Buczynski: Gorenstein schemes, smoothability and equations for secant
varieties

17:30-18:00 Alessandro Oneto: A Waring problem with higher degree terms