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BEGIN:VEVENT
SUMMARY:Rosa Winter (Leiden University)
DTSTART;VALUE=DATE-TIME:20200414T150000Z
DTEND;VALUE=DATE-TIME:20200414T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/1
DESCRIPTION:Title: Rational points on del Pezzo surfaces of degree 1\nby R
osa Winter (Leiden University) as part of Max Planck Institute nonlinear a
lgebra seminar\n\n\nAbstract\nDel Pezzo surfaces are classified by their d
egree\, an integer between 1 and 9. Famous examples are those of degree 3\
, which are cubic surfaces in đ3. In this talk I will focus on del Pezz
o surfaces of degree 1. After briefly describing their geometry\, I will t
alk about the set of Q-valued (rational) points on such a surface. I will
show what is known about this set so far\, and which questions are still o
pen.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Alexandr (University of California at Berkeley)
DTSTART;VALUE=DATE-TIME:20200414T154000Z
DTEND;VALUE=DATE-TIME:20200414T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/2
DESCRIPTION:Title: Logarithmic Voronoi cells\nby Yulia Alexandr (Universit
y of California at Berkeley) as part of Max Planck Institute nonlinear alg
ebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Szendroi (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200414T162000Z
DTEND;VALUE=DATE-TIME:20200414T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/3
DESCRIPTION:Title: The punctual Hilbert scheme of 4 points in affine 3-spa
ce\nby Balazs Szendroi (University of Oxford) as part of Max Planck Instit
ute nonlinear algebra seminar\n\n\nAbstract\nThe $n$-th punctual Hilbert s
cheme $\\operatorname{Hilb}^n_0(\\mathbb{A}^d)$ of points of affine $d$-sp
ace parametrises ideals of finite co-length $n$ of the ring of functions o
n $d$-dimensional affine space\, whose radical is the maximal ideal at the
origin (equivalently\, subschemes of length $n$ with support at the origi
n). A classical theorem of Briancon claims the irreducibility of this spac
e for $d=2$ and arbitrary $n$. The case of a small number of points being
straightforward\, the first nontrivial case is the case of $4$ points in $
3$-space. We show\, answering a question of Sturmfels\, that over the comp
lex numbers $\\operatorname{Hilb}^4_0(\\mathbb{A}^3)$ is irreducible. We u
se a combination of arguments from computer algebra and representation the
ory.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Nicklasson (Stockholm University)
DTSTART;VALUE=DATE-TIME:20200416T150000Z
DTEND;VALUE=DATE-TIME:20200416T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/4
DESCRIPTION:Title: Subalgebras of a polynomial ring with minimal Hilbert f
unction\nby Lisa Nicklasson (Stockholm University) as part of Max Planck I
nstitute nonlinear algebra seminar\n\n\nAbstract\nIn a recent paper by Boi
j and Conca the upper and lower bounds for the Hilbert function of subalge
bras of a polynomial ring are discussed. In this talk we will study subalg
ebras generated in degree two with minimal Hilbert function. These subalge
bras are generated by strongly stable sets of monomials. To minimize the H
ilbert function we want to firstly minimize the numbers of variables\, and
secondly the multiplicity of the algebra. This boils down to a purely com
binatorial problem\, as the multiplicity can be computed by counting the n
umber of maximal north-east lattice paths in an diagram representing the s
trongly stable set.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tara Fife (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20200416T154000Z
DTEND;VALUE=DATE-TIME:20200416T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/5
DESCRIPTION:Title: A friendly Introduction to matroids\nby Tara Fife (Loui
siana State University) as part of Max Planck Institute nonlinear algebra
seminar\n\n\nAbstract\nMatroids were introduced by Whitney in 1935 to prov
ide an abstract generalization of the notion of linear independence. Whitn
ey noted that matroids arise naturally from graphs and from matrices. More
recently\, people have discovered ties to matroid theory and algebraic ge
ometry. In this talk\, I will first introduce matroid theory\, along with
some key examples\, and central questions. I will then discuss connections
between matroid theory and nonlinear algebra.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:JosĂ© Samper (MPI MIS\, Leipzig)
DTSTART;VALUE=DATE-TIME:20200416T162000Z
DTEND;VALUE=DATE-TIME:20200416T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/6
DESCRIPTION:Title: Some shelling orders are better than others\nby JosĂ© S
amper (MPI MIS\, Leipzig) as part of Max Planck Institute nonlinear algebr
a seminar\n\n\nAbstract\nA shelling order is a recursive way of constructi
ng a polyhedral complex that helps to understand several topological\, alg
ebraic and combinatorial invariants. Consequently\, a significant amount o
f effort has been put into developing techniques to determine if a given c
omplex has a shelling order. In this talk we will explore a different poin
t of view that is less popular: for a complex that admits many shelling or
ders\, a good choice of the shelling order can can make a significant diff
erence. We address this problem for matroid independence complexes\, prese
nt an intriguing connection with shelling orders of polytopes\, and discus
s some experiments aimed at better understanding some old problems. This i
s based on joint work Alex Heaton.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Seigal (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200421T150000Z
DTEND;VALUE=DATE-TIME:20200421T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/7
DESCRIPTION:Title: Torus actions and maximum likelihood estimation\nby Ann
a Seigal (University of Oxford) as part of Max Planck Institute nonlinear
algebra seminar\n\n\nAbstract\nWe describe connections between invariant t
heory and maximum likelihood estimation\, in the context of log-linear mod
els. Finding a maximum likelihood estimate (MLE) is an optimisation proble
m over a statistical model\, to obtain the point that best fits observed d
ata. We show that this is equivalent to a capacity problem - finding the p
oint of minimal norm in an orbit under a corresponding torus action. The e
xistence of the MLE can then be characterized by stability under the actio
n. Moreover\, algorithms from statistics can be used in invariant theory\,
and vice versa. Based on joint work with Carlos AmĂ©ndola\, KathlĂ©n Kohn
and Philipp Reichenbach. This is part one of a two part talk: in the seco
nd part\, Philipp Reichenbach will discuss our results for multivariate Ga
ussian models.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Reichenbach (Technical University Berlin)
DTSTART;VALUE=DATE-TIME:20200421T154000Z
DTEND;VALUE=DATE-TIME:20200421T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/8
DESCRIPTION:Title: Invariant Theory and Matrix Normal Models\nby Philipp R
eichenbach (Technical University Berlin) as part of Max Planck Institute n
onlinear algebra seminar\n\n\nAbstract\nWe describe connections between in
variant theory and maximum likelihood estimation (ML estimation)\, in the
context of matrix normal models. Namely\, we link ML estimation in that ca
se to the left right action of SLxSL on tuples of matrices. This enables u
s to characterize ML estimation by stability under that group action. Furt
hermore\, invariant theory provides a new upper bound on the sample size f
or generic boundedness of the log-likelihood function. To illuminate the t
heory the talk puts emphasis on several examples. At the end we briefly ou
tline how our results generalize to Gaussian group models.\n\nBased on joi
nt work with Carlos AmĂ©ndola\, KathlĂ©n Kohn and Anna Seigal. This is the
second part of a two part talk: in the first part\, Anna Seigal will disc
uss our results for log-linear models.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aida Maraj (University of Kentucky)
DTSTART;VALUE=DATE-TIME:20200421T162000Z
DTEND;VALUE=DATE-TIME:20200421T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/9
DESCRIPTION:Title: The Equivariant Hilbert Series of Hierarchical Models\n
by Aida Maraj (University of Kentucky) as part of Max Planck Institute non
linear algebra seminar\n\n\nAbstract\nA hierarchical model is realizable b
y a simplicial complex that describes the dependency relationships among r
andom variables and the number of states of each random variable. Diaconis
and Sturmfels have constructed toric ideals that provide useful informati
on about the model. This talk concerns quantitative properties for familie
s of ideals arising from hierarchical models with the same dependency rela
tions and varying number of states. We introduce and study invariant filtr
ations of such ideals\, and their equivariant Hilbert series. A condition
that guarantees this multivariate series is a rational function will be pr
esented. The key is to construct finite automata that recognize languages
corresponding to invariant filtrations. Lastly\, we show that one can simi
larly prove the rationality of an equivariant Hilbert series for some filt
rations of algebras. This is joint work with Uwe Nagel.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ruddy (MPI MIS\, Leipzig)
DTSTART;VALUE=DATE-TIME:20200423T150000Z
DTEND;VALUE=DATE-TIME:20200423T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/10
DESCRIPTION:Title: Equivalence classes of planar algebraic curves through
numerical algebraic geometry\nby Michael Ruddy (MPI MIS\, Leipzig) as part
of Max Planck Institute nonlinear algebra seminar\n\n\nAbstract\nFor the
action of a group on the plane\, the group equivalence problem for curves
can be stated as: given two curves\, decide if they are related by an elem
ent of the group. We describe an efficient equality test\, using tools fro
m numerical algebraic geometry\, to determine (with âprobability-oneâ)
whether or not two rational maps have the same image up to Zariski closur
e. Using signature maps\, constructed from differential and joint invarian
ts\, we apply this test to solve the group equivalence problem for algebra
ic curves under the linear action of algebraic groups. In this talk I will
discuss the equality test and signature maps for algebraic curves\, focus
ing on the action of the complex Euclidean group for our computations and
examples. I will present some of our results comparing the sensitivity of
different signature maps. This is based on joint work with Tim Duff.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Brustenga i Moncusi (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20200423T154000Z
DTEND;VALUE=DATE-TIME:20200423T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/11
DESCRIPTION:Title: Reaction networks and toric systems\nby Laura Brustenga
i Moncusi (University of Copenhagen) as part of Max Planck Institute nonl
inear algebra seminar\n\n\nAbstract\nMass-action networks (edge labelled d
irected graphs) model cascades of chemical reactions (e.g. used by biologi
cal systems for adapting to the environment). From the assumption of mass-
action kinetics\, a mass-action network gives rise to a polynomial dynamic
al system. In this large class of polynomial systems\, the intuition from
Chemistry and Algebraic Geometry feed themselves\, giving exciting new res
ults. For example\, we will discuss complex balanced mass-action networks\
, which have a natural chemical interpretation and (conjecturally) complet
ely determines the dynamics of the associated systems (called toric dynami
cal systems). We will introduce âdisguised toric systemsâ\, which expl
oit this relationship the other way around: given a dynamical system\, can
we build a complex balanced mass-action network for it?\n\n(Joint work wi
th Gheorghe Craciun and Miruna-Ćtefana Sorea).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taylor Brysiewicz (Texas A&M)
DTSTART;VALUE=DATE-TIME:20200423T162000Z
DTEND;VALUE=DATE-TIME:20200423T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/12
DESCRIPTION:Title: Solving decomposable sparse systems\nby Taylor Brysiewi
cz (Texas A&M) as part of Max Planck Institute nonlinear algebra seminar\n
\n\nAbstract\nAmendola et al. proposed a method for solving systems of pol
ynomial equations lying in a family which exploits a recursive decompositi
on into smaller systems. A family of systems admits such a decomposition i
f and only if the corresponding monodromy group is imprimitive. A conseque
nce of Esterovâs classification of sparse polynomial systems with imprim
itive monodromy groups is that this decomposition is obtained by inspectio
n. Using these ideas\, we present a recursive algorithm to numerically sol
ve decomposable sparse systems. This is joint work with Frank Sottile\, Jo
se Rodriguez\, and Thomas Yahl.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sascha Timme (Technical University Berlin)
DTSTART;VALUE=DATE-TIME:20200430T150000Z
DTEND;VALUE=DATE-TIME:20200430T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/13
DESCRIPTION:Title: 3264 Conics in a Second\nby Sascha Timme (Technical Uni
versity Berlin) as part of Max Planck Institute nonlinear algebra seminar\
n\n\nAbstract\nEnumerative algebraic geometry counts the solutions to cert
ain geometric constraints. Numerical algebraic geometry determines these s
olutions for any given instance. In this talk I want to illustrate how the
se two fields complement each other. The focus lies on the 3264 conics tha
t are tangent to five given conics in the plane. I will illustrate tools a
nd techniques used in numerical algebraic geometry and how we used these t
o find a fully real instance of this classic problem.\n\nThis is joint wor
k with P. Breiding and B. Sturmfels.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Theran (University of St. Andrews)
DTSTART;VALUE=DATE-TIME:20200409T154000Z
DTEND;VALUE=DATE-TIME:20200409T162000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/14
DESCRIPTION:Title: Graph rigidity and measurement varieties\nby Louis Ther
an (University of St. Andrews) as part of Max Planck Institute nonlinear a
lgebra seminar\n\n\nAbstract\nGeometric rigidity theory is concerned with
how much information about a configuration p of n points in a d-dimensiona
l Euclidean space is determined by pairwise Euclidean distance measurement
s\, indexed by the edges of a graph G with n vertices. One can turn this a
round\, and\, define\, for a fixed graph G\, a âmeasurement variety" ass
ociated with all possible edge lengths measurements as the configuration v
aries. Iâll survey some (somewhat) recent results in geometric rigidity
obtained by studying the geometry of measurement varieties.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenie Hunsicker (Loughborough University)
DTSTART;VALUE=DATE-TIME:20200409T162000Z
DTEND;VALUE=DATE-TIME:20200409T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/15
DESCRIPTION:Title: Architecture for the Working Mathematician\nby Eugenie
Hunsicker (Loughborough University) as part of Max Planck Institute nonlin
ear algebra seminar\n\n\nAbstract\nDel Pezzo surfaces are classified by th
eir degree\, an integer between 1 and 9. Famous examples are those of degr
ee 3\, which are cubic surfaces in $P ^ 3$. In this talk I will focus on d
el Pezzo surfaces of degree 1. After briefly describing their geometry\, I
will talk about the set of Q-valued (rational) points on such a surface.
I will show what is known about this set so far\, and which questions are
still open.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joscha Diehl (UniversitĂ€t Greifswald)
DTSTART;VALUE=DATE-TIME:20200428T150000Z
DTEND;VALUE=DATE-TIME:20200428T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/16
DESCRIPTION:Title: Time warping invariants and quasisymmetric functions\nb
y Joscha Diehl (UniversitĂ€t Greifswald) as part of Max Planck Institute n
onlinear algebra seminar\n\n\nAbstract\nThe analysis of time series is a s
tandard task in data science. Usually\, as a first step\, features of a ti
me series must be extracted that characterize the series\, maybe modulo ir
relevant (depending on the application) group actions on the original data
. In this talk I will discuss the action of time-warping: the features sho
uld be invariant to the speed at which the time-series is run through. Thi
s leads\, as we show\, to quasisymmetric functions\, and I discuss their H
opf algebraic setup.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Bik (UniversitĂ€t Bern)
DTSTART;VALUE=DATE-TIME:20200428T154000Z
DTEND;VALUE=DATE-TIME:20200428T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/17
DESCRIPTION:Title: Polynomial functors as affine spaces\nby Arthur Bik (Un
iversitĂ€t Bern) as part of Max Planck Institute nonlinear algebra seminar
\n\n\nAbstract\nPolynomial functors are like spaces of objects (e.g. k-way
tensors) without fixed size and come with an action of (products of) gene
ral linear groups. The aim of this talk is to answer the following questio
n: what happens when you replace vector spaces by polynomial functors when
defining affine spaces?\n\nI will define polynomial functors\, the maps b
etween them and their Zariski-closed subsets and give examples of these th
ings. Then\, I will discuss how to extend some of the basic results from a
ffine algebraic geometry to this setting. This is joint work with Jan Drai
sma\, Rob Eggermont and Andrew Snowden.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas KĂŒhne (The Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20200428T162000Z
DTEND;VALUE=DATE-TIME:20200428T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/18
DESCRIPTION:Title: Generalised Matroid Representations: Universality and D
ecidability\nby Lukas KĂŒhne (The Hebrew University of Jerusalem) as part
of Max Planck Institute nonlinear algebra seminar\n\n\nAbstract\nA matroid
is a combinatorial object based on an abstraction of linear independence
in vector spaces and forests in graphs. It is a classical question to dete
rmine whether a given matroid is representable as a vector configuration o
ver a field. Such a matroid is called linear.\n\nThis talk addresses gener
alisations of such representations over division rings or matrix rings whi
ch are called skew linear and multilinear matroids respectively.We will de
scribe a generalised Dowling geometry that encodes non commutative equatio
ns in matroids. This construction allows us to reduce word problem instanc
es to skew linear or multilinear matroid representations.\n\nThe talk is b
ased on joint work with Rudi Pendavingh and Geva Yashfe.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Sottile (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20200430T154000Z
DTEND;VALUE=DATE-TIME:20200430T161000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/19
DESCRIPTION:Title: Galois groups in Enumerative Geometry and Applications\
nby Frank Sottile (Texas A&M University) as part of Max Planck Institute n
onlinear algebra seminar\n\n\nAbstract\nIn 1870 Jordan explained how Galoi
s theory can be applied to problems from enumerative geometry\, with the g
roup encoding intrinsic structure of the problem. Earlier Hermite showed t
he equivalence of Galois groups with geometric monodromy groups\, and in 1
979 Harris initiated the modern study of Galois groups of enumerative prob
lems. He posited that a Galois group should be âas large as possibleâ
in that it will be the largest group preserving internal symmetry in the g
eometric problem.\n\nI will describe this background and discuss some work
in a long-term project to compute\, study\, and use Galois groups of geom
etric problems\, including those that arise in applications of algebraic g
eometry. A main focus is to understand Galois groups in the Schubert calcu
lus\, a well-understood class of geometric problems that has long served a
s a laboratory for testing new ideas in enumerative geometry.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khazhgali Kozhasov (Technical University Braunschweig)
DTSTART;VALUE=DATE-TIME:20200430T162000Z
DTEND;VALUE=DATE-TIME:20200430T165000Z
DTSTAMP;VALUE=DATE-TIME:20201031T043822Z
UID:NASO/20
DESCRIPTION:Title: On Minimality of Determinantal Varieties\nby Khazhgali
Kozhasov (Technical University Braunschweig) as part of Max Planck Institu
te nonlinear algebra seminar\n\n\nAbstract\nMinimal submanifolds are mathe
matical abstractions of soap films: they minimize the Riemannian volume lo
cally around every point. Finding minimal algebraic hypersurfaces in đ
đ for each n is a long-standing open problem posed by Hsiang. In 2010 T
kachev gave a partial solution to this problem showing that the hypersurfa
ce of n x n real matrices of corank one is minimal. I will discuss the fol
lowing generalization of this fact to all determinantal matrix varieties:
for any m\, n and r