BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201021T183000Z
DTEND:20201021T193000Z
DTSTAMP:20260404T095548Z
UID:Lecture_series_NT_AG/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Lectu
 re_series_NT_AG/1/">An application of random plane slicing to counting $\\
 mathbb{F}_q$-points on hypersurfaces</a>\nby Kaloyan Slavov (ETH Zurich) a
 s part of Lecture series in number theory and algebraic geometry\n\n\nAbst
 ract\nWe first review the classical Lang--Weil bound on the number of $\\m
 athbb{F}_q$-points on a geometrically irreducible hypersurface $X$ over a 
 finite field $\\mathbb{F}_q$. By studying the intersection of $X(\\mathbb{
 F}_q)$ with a random $\\mathbb{F}_q$-plane\, we improve the best known bou
 nds in the literature for $|X(\\mathbb{F}_q)|$.\n
LOCATION:https://stable.researchseminars.org/talk/Lecture_series_NT_AG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201026T200000Z
DTEND:20201026T210000Z
DTSTAMP:20260404T095548Z
UID:Lecture_series_NT_AG/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Lectu
 re_series_NT_AG/2/">A refinement of Bertini irreducibility via point-count
 ing over finite fields</a>\nby Kaloyan Slavov (ETH Zurich) as part of Lect
 ure series in number theory and algebraic geometry\n\n\nAbstract\nWe appro
 ach classical Bertini irreducibility theorems over an arbitrary algebraica
 lly closed field through a reduction to point-counting over finite fields 
 and a probabilistic combinatorial argument based on random hyperplane slic
 ing. A classical theorem by Bertini states that if $X\\subset\\mathbb{P}^n
 $ is an irreducible variety of dimension at least $2$\, then there is a de
 nse open subset $M_{\\text{good}}$ inside the space \n$\\check{\\mathbb{P}
 }^n$ of hyperplanes in $\\mathbb{P}^n$ such that $X\\cap H$ is irreducible
  for each $H$ in $M_{\\text{good}}$. Benoist proved that in fact\, the com
 plement of $M_{\\text{good}}$ in \n$\\check{\\mathbb{P}}^n$ has dimension 
 at most $\\operatorname{codim} X+1$. We give a new proof of this\, along w
 ith a refinement in which the embedding $X\\hookrightarrow\\mathbb{P}^n$ i
 s replaced by a more general morphism $X\\to\\mathbb{P}^n$. This is joint 
 work with Bjorn Poonen.\n
LOCATION:https://stable.researchseminars.org/talk/Lecture_series_NT_AG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201028T183000Z
DTEND:20201028T193000Z
DTSTAMP:20260404T095548Z
UID:Lecture_series_NT_AG/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Lectu
 re_series_NT_AG/3/">The moduli space of hypersurfaces whose singular locus
  has high dimension</a>\nby Kaloyan Slavov (ETH Zurich) as part of Lecture
  series in number theory and algebraic geometry\n\n\nAbstract\nConsider th
 e moduli space of hypersurfaces of degree $\\ell$ in $\\mathbb{P}^n$ whose
  singular locus has dimension at least $b$ (for a fixed $b\\geq 1$). We pr
 ove that when $\\ell$ is large\, this moduli space has a unique irreducibl
 e component of maximal dimension\, consisting of the hypersurfaces singula
 r along a linear $b$-​dimensional space. The proof will involve a reduct
 ion to positive characteristic and a probabilistic counting argument over 
 finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/Lecture_series_NT_AG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201102T210000Z
DTEND:20201102T220000Z
DTSTAMP:20260404T095548Z
UID:Lecture_series_NT_AG/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Lectu
 re_series_NT_AG/4/">What is the probability that a random (sparse) polynom
 ial of degree $d$ over a finite field is irreducible?</a>\nby Kaloyan Slav
 ov (ETH Zurich) as part of Lecture series in number theory and algebraic g
 eometry\n\n\nAbstract\nA classical result of Gauss states that among all m
 onic polynomials of degree $d$ over a finite field\,\napproximately $1/d$ 
 are irreducible. Extending previous results in the literature\, we prove t
 hat under a mild assumption\, the proportion of irreducible polynomials do
 es not change even if only the last two coefficients are allowed to vary. 
 Our approach is geometric. The talk will be nontechnical and accessible to
  a broad audience.\n
LOCATION:https://stable.researchseminars.org/talk/Lecture_series_NT_AG/4/
END:VEVENT
END:VCALENDAR