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BEGIN:VEVENT
SUMMARY:Shushi Harashita (Yokohama National University)
DTSTART;VALUE=DATE-TIME:20201013T005000Z
DTEND;VALUE=DATE-TIME:20201013T015000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/1
DESCRIPTION:Title: Supersingular abelian varieties and curves\, and their modul
i spaces\nby Shushi Harashita (Yokohama National University) as part o
f RIMS conference: Theory and Applications of Supersingular Curves and Sup
ersingular Abelian Varieties\n\n\nAbstract\nIn this talk\, we give a revie
w of fundamentals of supersingular/superspecial abelian varieties and curv
es. After we recall the definition and basic properties of them\, we expla
in some known results on the supersingular locus in the moduli space of po
larized abelian varieties and on natural stratifications on it. Finally\,
we discuss the intersection of the supersingular locus and the Torelli loc
us in the lower genus case ($g \\leq 4$).\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyoshi Ibukiyama (Osaka University)
DTSTART;VALUE=DATE-TIME:20201013T021000Z
DTEND;VALUE=DATE-TIME:20201013T031000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/2
DESCRIPTION:Title: Supersingular loci of low dimensions and parahoric subgroups
\nby Tomoyoshi Ibukiyama (Osaka University) as part of RIMS conference
: Theory and Applications of Supersingular Curves and Supersingular Abelia
n Varieties\n\n\nAbstract\nIt is known by F. Oort and his collaborators th
at several geometric invariants of the supersingular locus of principally
polarized abelian varieties are closely connected to arithmetic invariants
of some quaternion hermitian forms. In the present talk\, when dimension
is $2$ or $3$\, we characterize subsets of "$\\dim Hom(\\alpha_p\, A) > 1$
" parts in each connected component by adelic double cosets of the quatern
ion hermitian group with respect to some parahoric subgroups\, and then ch
aracterize their configuration by non-emptyness of intersections of the co
rresponding double cosets. For example we can answer by this on which comp
onents a given principally polarized superspecial abelian variety lies.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chia-Fu Yu (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20201013T050000Z
DTEND;VALUE=DATE-TIME:20201013T060000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/3
DESCRIPTION:Title: Polarized simple superspecial abelian surfaces with real Wei
l numbers\nby Chia-Fu Yu (Academia Sinica) as part of RIMS conference:
Theory and Applications of Supersingular Curves and Supersingular Abelian
Varieties\n\n\nAbstract\nIn this talk I will present explicit formulas fo
r\n\n(1) the number of superspecial abelian surfaces over $\\mathbb{F}_p$
with Frobenius endomorphism $\\sqrt{p}$ equipped with a polarization modul
e\;\n\n(2) the type number of a genus of them\;\n\n(3) the refined class a
nd type numbers of the subset with a fixed automorphism group.\nOur formul
as suggest a mysterious connection with arithmetic genera of Hilbert modul
ar surfaces. This is based on joint work with Jiangwei Xue.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Stefan Koskivirta (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201013T062000Z
DTEND;VALUE=DATE-TIME:20201013T072000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/4
DESCRIPTION:Title: Abelian varieties and stacks of G-zips\nby Jean-Stefan K
oskivirta (The University of Tokyo) as part of RIMS conference: Theory and
Applications of Supersingular Curves and Supersingular Abelian Varieties\
n\n\nAbstract\nFor a reductive group $G$\, the stack of $G$-zips was defin
ed by Pink-Wedhorn-Ziegler. It is an algebraic stack defined over a field
of characteristic $p$. It is a group-theoretical object which detects the
isomorphism class of the $p$-torsion of the abelian variety (possibly endo
wed with some additional structure). We will explain how the stack of $G$-
zips makes it possible to construct generalized Hasse invariants. We also
explain some applications regarding ampleness of line bundles and affinene
ss of strata.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiyuki Katsura (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201013T074000Z
DTEND;VALUE=DATE-TIME:20201013T084000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/5
DESCRIPTION:Title: On the classification of Enriques surfaces with finite autom
orphism group\nby Toshiyuki Katsura (The University of Tokyo) as part
of RIMS conference: Theory and Applications of Supersingular Curves and Su
persingular Abelian Varieties\n\n\nAbstract\nIn characteristic $0$\, S. Ko
ndo classified the Enriques surfaces with finite automorphism group into s
even types. In characteristic $p \\geq 3$\, the situation is similar\, but
in characteristic $2$\, the situation is very different. In this talk\, w
e first give a survey of the results in characteristic $0$. Then\, for the
Enriques surfaces with finite automorphism group in characteristic $2$\,
we give the complete classification of them. We have 3 types for singular
Enriques surfaces\, 5 types for supersingular Enriques surfaces and 8 type
s for classical Enriques surfaces. This is a joint work with S. Kondo and
G. Martin.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Everett W. Howe (Unaffiliated)
DTSTART;VALUE=DATE-TIME:20201014T005000Z
DTEND;VALUE=DATE-TIME:20201014T015000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/6
DESCRIPTION:Title: Constructions for supersingular and superspecial curves\
nby Everett W. Howe (Unaffiliated) as part of RIMS conference: Theory and
Applications of Supersingular Curves and Supersingular Abelian Varieties\n
\n\nAbstract\nOne way of producing supersingular or superspecial curves ov
er a finite field is to examine constructions of curves whose Jacobians ar
e known to be isogenous to products of lower-dimensional varieties. We wil
l look at two different strategies for producing supersingular or superspe
cial curves in such families: One can look at specific curves in character
istic zero whose reductions modulo certain primes are necessarily supersin
gular or superspecial\, or one can look at families that are large enough
so that one expects (and\, hopefully\, can prove) that there are supersing
ular or superspecial curves in the family.\nWe show\, for example\, that f
or $g$ equal to $5$\, $7$\, $9$\, and 11 there are infinitely many primes
$p$ for which there exist superspecial curves of genus $g$\, and we look a
t some constructions in lower genus that one might hope will produce super
singular or superspecial curves for every characteristic.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Momonari Kudo (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201014T021000Z
DTEND;VALUE=DATE-TIME:20201014T031000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/7
DESCRIPTION:Title: Counting the isomorphism classes of superspecial curves\
nby Momonari Kudo (The University of Tokyo) as part of RIMS conference: Th
eory and Applications of Supersingular Curves and Supersingular Abelian Va
rieties\n\n\nAbstract\nThis talk is devoted to a survey of the study on co
unting the number of isomorphism classes of superspecial curves. In the ca
se of genus $3$ or less\, it follows from a general result by Ibukiyama-Ka
tsura-Oort on superspecial principally polarized abelian varieties that th
e number (over an algebraically closed field) is determined by computing t
he class numbers of quaternion hermitian lattices. On the one hand\, the p
roblem for genus $4$ or more has not been solved in all primes\, but in re
cent years\, I and Harashita developed several algorithms to count genus $
4$ or $5$ superspecial curves. The first part of this talk aims to review
the case of genus $3$ or less\, and our results (for small primes) obtaine
d by the algorithms in the case of genus $4$ and $5$. In the second part\,
I describe the most recent result by a joint work with Harashita and Howe
\, where we presented algorithms to count (or find) superspecial curves am
ong a $2$-dimensional family of genus $4$ non-hyperelliptic curves.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Aikawa (Mitsubishi Electric)
DTSTART;VALUE=DATE-TIME:20201014T050000Z
DTEND;VALUE=DATE-TIME:20201014T060000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/8
DESCRIPTION:Title: Post-quantum cryptography from supersingular isogenies\n
by Yusuke Aikawa (Mitsubishi Electric) as part of RIMS conference: Theory
and Applications of Supersingular Curves and Supersingular Abelian Varieti
es\n\n\nAbstract\nPost-quantum cryptography is a next-generation public-ke
y cryptosystem that resistant to cryptoanalysis by both classical and quan
tum computers. Isogenies between supersingular elliptic curves present one
promising candidate\, which is called isogeny-based cryptography. In this
talk\, we will explain recent development in isogeny-based cryptography\,
mainly focusing on two standard key exchange protocols called SIDH scheme
and CSIDH scheme\, as well as our related results.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Onuki (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201014T062000Z
DTEND;VALUE=DATE-TIME:20201014T072000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/9
DESCRIPTION:Title: OSIDH and SiGamal: cryptosystems from supersingular elliptic
curves\nby Hiroshi Onuki (The University of Tokyo) as part of RIMS co
nference: Theory and Applications of Supersingular Curves and Supersingula
r Abelian Varieties\n\n\nAbstract\nThis talk will introduce relatively new
two cryptosystems based on isogenies between supersingular elliptic curve
s: OSIDH and SiGamal. OSIDH uses the action of the ideal class group of an
order in an imaginary quadratic field on supersingular elliptic curves. T
he endomorphism rings of these curves have a subring isomorphic to the ord
er. SiGamal is based on an assumption that the image of a point under an i
sogeny is as hard to calculate as the isogeny itself. I will give the theo
retical background of these cryptosystems and related mathematical problem
s.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wouter Castryck (KU Leuven)
DTSTART;VALUE=DATE-TIME:20201014T074000Z
DTEND;VALUE=DATE-TIME:20201014T084000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/10
DESCRIPTION:Title: Isogenies between supersingular elliptic curves over finite
prime fields\nby Wouter Castryck (KU Leuven) as part of RIMS conferen
ce: Theory and Applications of Supersingular Curves and Supersingular Abel
ian Varieties\n\n\nAbstract\nThe main goal of this talk will be to give a
survey of our current understanding of how the set of supersingular ellipt
ic curves over a finite prime field $\\mathbb{F}_p$ is connected by $\\mat
hbb{F}_p$-rational isogenies\, both from a theoretical and an algorithmic
point of view. This will discuss results by a.o. Delfs-Galbraith\, Schoof
and Waterhouse. Along the way I will mention joint work with Lorenz Panny\
, Jana Sotakova and Frederik Vercauteren.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce W. Jordan (The City University of New York)
DTSTART;VALUE=DATE-TIME:20201014T233000Z
DTEND;VALUE=DATE-TIME:20201015T003000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/11
DESCRIPTION:Title: Isogeny graphs of superspecial abelian varieties\nby Br
uce W. Jordan (The City University of New York) as part of RIMS conference
: Theory and Applications of Supersingular Curves and Supersingular Abelia
n Varieties\n\n\nAbstract\nThis talk is the first of two at the conference
on our recent connectedness theorem in “Isogeny graphs of superspecial
abelian varieties and generalized Brandt matrices”\, Bruce W. Jordan and
Yevgeny Zaytman\, arXiv:2005.09031\, 18 May 2020. It will explain the nec
essary background on principally polarized superspecial abelian varieties
and their isogenies. We will define three different isogeny graphs and dis
cuss their p-adic uniformizations and how their adjacency matrices are (ge
neralized) Brandt matrices. For $g = 1$ we will explain another occurrence
of precisely these graphs in arithmetic geometry – as the dual graph of
the bad reduction of Shimura curves. This raises the interesting question
of the relationship of our isogeny graphs for higher dimensions $g > 1$ t
o vanishing cycles and the bad reduction of Shimura varieties.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yevgeny Zaytman (Center for Communications Research)
DTSTART;VALUE=DATE-TIME:20201015T005000Z
DTEND;VALUE=DATE-TIME:20201015T015000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/12
DESCRIPTION:Title: Proving connectedness of isogeny graphs with strong approxi
mation\nby Yevgeny Zaytman (Center for Communications Research) as par
t of RIMS conference: Theory and Applications of Supersingular Curves and
Supersingular Abelian Varieties\n\n\nAbstract\nThis talk is the second of
two at the conference on our recent connectedness theorem in “Isogeny gr
aphs of superspecial abelian varieties and generalized Brandt matrices”\
, Bruce W. Jordan and Yevgeny Zaytman\, arXiv:2005.09031\, 18 May 2020. It
is well known that the isogeny graphs of supersingular elliptic curves ar
e connected and Ramanujan. For superspecial abelian varieties in higher di
mension we show that the isogeny graphs are connected but not in general R
amanujan. This talk will explain the proof of the connectedness result. We
will review the strong approximation theorem for algebraic groups and the
n apply it to the quaternionic unitary group to obtain our connectedness r
esult. We will conclude by giving examples as time permits\, showing that
the isogeny graph for Richelot isogenies for dimension $g = 2$ in characte
ristic $11$ is not Ramanujan\, whereas it is Ramanujan in characteristics
$5$ and $7$.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungrok Jo (University of Tsukuba)
DTSTART;VALUE=DATE-TIME:20201015T021000Z
DTEND;VALUE=DATE-TIME:20201015T031000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/13
DESCRIPTION:Title: On generalized LPS Ramanujan graphs and Bruhat-Tits trees\nby Hyungrok Jo (University of Tsukuba) as part of RIMS conference: The
ory and Applications of Supersingular Curves and Supersingular Abelian Var
ieties\n\n\nAbstract\nIt is introduced a generalized version of explicit c
onstructions of Lubotzky\, Phillips\, Sarnak’s Ramanujan graphs (in shor
t\, LPS-type graphs) in MQC2019 (International Symposium on Mathematics\,
Quantum Theory\, and Cryptography 2019). In this talk\, we interpret a ver
y concrete example of LPS-type graphs as Bruhat-Tits trees. We also give a
brief comparison of LPS-type graphs and Pizer’s graphs\, known as a sup
ersingular isogeny graph (SSIG).\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masaya Yasuda and Kazuhiro Yokoyama (Rikkyo University)
DTSTART;VALUE=DATE-TIME:20201015T050000Z
DTEND;VALUE=DATE-TIME:20201015T060000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/14
DESCRIPTION:Title: Introduction to algebraic approaches for solving isogeny pa
th-finding problems\nby Masaya Yasuda and Kazuhiro Yokoyama (Rikkyo Un
iversity) as part of RIMS conference: Theory and Applications of Supersing
ular Curves and Supersingular Abelian Varieties\n\n\nAbstract\nIn recent y
ears\, supersingular isogeny cryptosystems have received attention as a ca
ndidate of post-quantum cryptography. Their security relies on the computa
tional hardness of solving isogeny problems over supersingular elliptic cu
rves. In the first part of this talk\, we give a brief survey on isogeny p
roblems and the meet-in-the-middle approach for solving them. In the rest
of this talk\, we introduce algebraic approaches for solving isogeny probl
ems. Our basic idea is to reduce isogeny problems to a system of algebraic
equations and to solve it by Groebner basis computation.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsuyuki Takashima (Mitsubishi Electric)
DTSTART;VALUE=DATE-TIME:20201015T062000Z
DTEND;VALUE=DATE-TIME:20201015T072000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/15
DESCRIPTION:Title: Counting superspecial Richelot isogenies by reduced automor
phism groups\nby Katsuyuki Takashima (Mitsubishi Electric) as part of
RIMS conference: Theory and Applications of Supersingular Curves and Super
singular Abelian Varieties\n\n\nAbstract\nRecently\, supersingular ellipti
c curve isogeny cryptography has been extended to the genus-$2$ case by us
ing superspecial genus-$2$ curves and their Richelot isogeny graphs. In th
is talk\, in order to establish a firm ground for the cryptographic constr
uction and analysis\, we give a new characterization of decomposed Richelo
t isogenies in terms of involutive reduced automorphisms of genus-$2$ curv
es over a finite field\, and explicitly count such decomposed (and non-dec
omposed) Richelot isogenies up to isomorphism between superspecial princip
ally polarized abelian surfaces. As a corollary\, we give another algebrai
c geometric proof of Theorem 2 in the paper of Castryck et al.(Journal of
Math. Crypto. 2020). This is joint work with Toshiyuki Katsura.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Smith (INRIA)
DTSTART;VALUE=DATE-TIME:20201015T074000Z
DTEND;VALUE=DATE-TIME:20201015T084000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202601Z
UID:supersingular2020RIMS/16
DESCRIPTION:Title: Special structures and cryptosystems in the superspecial Ri
chelot isogeny graph\nby Benjamin Smith (INRIA) as part of RIMS confer
ence: Theory and Applications of Supersingular Curves and Supersingular Ab
elian Varieties\n\n\nAbstract\nIn this talk\, we consider the graph formed
by (isomorphism classes of) superspecial principally polarized abelian su
rfaces and the Richelot isogenies between them. This is a natural generali
zation of the graph of supersingular elliptic curves connected by $2$-isog
enies\, and so we have natural generalizations of supersingular elliptic c
ryptosystems. But the combinatorial properties of the Richelot graph are m
ore complicated than those of the elliptic graph\, and there are large spe
cial structures within the Richelot graph that do not occur in the ellipti
c case. We will explore these special structures\, and their implications
for the statistics of random walks and the security of genus-$2$ isogeny-b
ased cryptosystems.\n
LOCATION:https://researchseminars.org/talk/supersingular2020RIMS/16/
END:VEVENT
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