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DTSTART:20290325T030000
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BEGIN:VEVENT
DTSTAMP:20261106T001140Z
UID:1794398400@ist.ac.at
DTSTART:20261111T130000
DTEND:20261111T140000
DESCRIPTION:Speaker: Katy Woo\nhosted by Vivian Kuperberg\nAbstract: There 
 is a long-standing history of using prime counting results to prove new th
 eorems about arithmetic objects\; Dirichlet’s theorem on primes in arith
 metic progressions was a key input in Hasse’s original proof of the loca
 l-to-global principle for quadratic forms over Q. In Corollary X.6.2.1 of 
 Silverman’s “The Arithmetic of Elliptic Curves”\, any elliptic curve
  of the form y^2 = x^3 + px for p a prime number congruent to 7 mod 16 is 
 shown to have rank zero\; Dirichlet’s theorem can be applied to show tha
 t there are infinitely many such elliptic curves. The breakthrough work of
  Green\, Tao\, and Ziegler on simultaneously prime values of linear system
 s was applied both to study Brauer-Manin obstructions to local-to-global p
 rinciples for certain conic bundles and to construct families of elliptic 
 curves with rank 1.In this talk\, we will build on the seminal work of Gre
 en and Sawhney to prove new instances of the multivariate Bateman-Horn con
 jecture\; the key input will be methods from additive combinatorics. We wi
 ll then discuss how to use these new prime counting results to study the B
 rauer-Manin obstruction to local-to-global principles for an expanded clas
 s of conic bundles and construct quadratic twist families of elliptic curv
 es with rank 2.This talk is based on joint work with Niven Achenjang.
LOCATION:Sunstone Bldg / Ground floor / Big Seminar Room A \, ISTA
ORGANIZER:
SUMMARY:Katy Woo: Arithmetic consequences of additive combinatorics
URL:https://talks-calendar.ista.ac.at/events/6675
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20261106T001140Z
UID:6a1e9cbf757f2024666156@ist.ac.at
DTSTART:20261124T150000
DTEND:20261124T160000
DESCRIPTION:Speaker: Bruno Nachtergaele\nhosted by Laszlo Erdös\nAbstract:
  I will review several recent results about the ground state gap of quantu
 m many-body systems and the question of spectral gap stability under pertu
 rbations. I will discuss results for the AKLT model on the hexagonal latti
 ce\, in particular the Local Quantum Topological Order (LTQO) property for
  it. The LTQO property will be further clarified by considering two one-di
 mensional models with multiple ground states: certain Haldane pseudopotent
 ials and the Temperley-Lieb spin chains. For the first I will present a ne
 w gap stability result. The latter provide examples of an unstable ground 
 state gap.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Bruno Nachtergaele: Stability of Gapped Ground States
URL:https://talks-calendar.ista.ac.at/events/6719
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