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:20260422T212834Z
UID:Lecture_series_NT_AG/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Lecture_seri
 es_NT_AG/1/">An application of random plane slicing to counting $\\mathbb{
 F}_q$-points on hypersurfaces</a>\nby Kaloyan Slavov (ETH Zurich) as part 
 of Lecture series in number theory and algebraic geometry\n\n\nAbstract\nW
 e first review the classical Lang--Weil bound on the number of $\\mathbb{F
 }_q$-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 bounds in 
 the literature for $|X(\\mathbb{F}_q)|$.\n
LOCATION:https://researchseminars.org/talk/Lecture_series_NT_AG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201026T200000Z
DTEND:20201026T210000Z
DTSTAMP:20260422T212834Z
UID:Lecture_series_NT_AG/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Lecture_seri
 es_NT_AG/2/">A refinement of Bertini irreducibility via point-counting ove
 r finite fields</a>\nby Kaloyan Slavov (ETH Zurich) as part of Lecture ser
 ies in number theory and algebraic geometry\n\n\nAbstract\nWe approach cla
 ssical Bertini irreducibility theorems over an arbitrary algebraically clo
 sed field through a reduction to point-counting over finite fields and a p
 robabilistic combinatorial argument based on random hyperplane slicing. 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 dense ope
 n 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 ea
 ch $H$ in $M_{\\text{good}}$. Benoist proved that in fact\, the complement
  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 with a r
 efinement in which the embedding $X\\hookrightarrow\\mathbb{P}^n$ is repla
 ced by a more general morphism $X\\to\\mathbb{P}^n$. This is joint work wi
 th Bjorn Poonen.\n
LOCATION:https://researchseminars.org/talk/Lecture_series_NT_AG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201028T183000Z
DTEND:20201028T193000Z
DTSTAMP:20260422T212834Z
UID:Lecture_series_NT_AG/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Lecture_seri
 es_NT_AG/3/">The moduli space of hypersurfaces whose singular locus has hi
 gh dimension</a>\nby Kaloyan Slavov (ETH Zurich) as part of Lecture series
  in number theory and algebraic geometry\n\n\nAbstract\nConsider the modul
 i space of hypersurfaces of degree $\\ell$ in $\\mathbb{P}^n$ whose singul
 ar locus has dimension at least $b$ (for a fixed $b\\geq 1$). We prove tha
 t when $\\ell$ is large\, this moduli space has a unique irreducible compo
 nent of maximal dimension\, consisting of the hypersurfaces singular along
  a linear $b$-​dimensional space. The proof will involve a reduction to 
 positive characteristic and a probabilistic counting argument over finite 
 fields.\n
LOCATION:https://researchseminars.org/talk/Lecture_series_NT_AG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (ETH Zurich)
DTSTART:20201102T210000Z
DTEND:20201102T220000Z
DTSTAMP:20260422T212834Z
UID:Lecture_series_NT_AG/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Lecture_seri
 es_NT_AG/4/">What is the probability that a random (sparse) polynomial of 
 degree $d$ over a finite field is irreducible?</a>\nby Kaloyan Slavov (ETH
  Zurich) as part of Lecture series in number theory and algebraic geometry
 \n\n\nAbstract\nA classical result of Gauss states that among all monic po
 lynomials of degree $d$ over a finite field\,\napproximately $1/d$ are irr
 educible. Extending previous results in the literature\, we prove that und
 er a mild assumption\, the proportion of irreducible polynomials does not 
 change even if only the last two coefficients are allowed to vary. Our app
 roach is geometric. The talk will be nontechnical and accessible to a broa
 d audience.\n
LOCATION:https://researchseminars.org/talk/Lecture_series_NT_AG/4/
END:VEVENT
END:VCALENDAR