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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3df6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260723T120000
DTEND;TZID=America/New_York:20260723T130000
CATEGORIES:Special Event
SUMMARY:Shai Pilosof: Predicting Species Interactions in Ecological
 Networks
DESCRIPTION:Kalaniyot Lunch and Learn\nplease\nRSVP for lunch
LOCATION:Haldeman 125
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BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3e83@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260814T100000
CATEGORIES:Thesis Defence
SUMMARY:Casey Dowdle: Electronic Structure Discretization and
 Compression Using Diagonal Basis Sets
DESCRIPTION:In this thesis\, we study the discretization and
 resulting compression of electronic Hamiltonians using diagonal
 basis sets. A diagonal basis set approximately diagonalizes the
 matrix and tensor representations of the one- and two-body
 potentials. This can reduce storage\, simplify matrix-vector
 products\, and lower the complexity of tensor network methods. Two
 important kinds of diagonal basis sets are studied: Discrete
 variable representation and gausslets.\n\nWe first give a background
 of quantum mechanics\, using quantum computing and probability as a
 motivation. We then set up the electronic structure problem in both
 first and second quantization. Different ground state numerical
 methods\, along with applications of basis set optimization\, are
 discussed.\n\nFor the rest of the thesis\, we focus on analysis of
 diagonal basis sets. We review two frameworks for diagonal
 approximations: Gaussian quadrature and the completeness\,
 orthogonality\, moment\, and X-diagonalization (COMX) properties.
 These frameworks are used to clarify the connection between discrete
 variable representation (DVR) and gausslets. We analyze and compare
 separable approximations of the Coulomb potential\, giving a simple
 parameter optimization method for term reduction. We also show how
 using a separable potential\, along with the diagonal
 approximation\, can significantly reduce memory cost for Fock
 matrix-vector products.\n\nFinally\, we end this thesis with a
 numerical study of both one- and three-dimensional quantum
 chemistry. One-dimensional chemistry serves as a model system\,
 where we demonstrate a clear advantage for diagonal basis sets over
 one-dimensional atomic orbitals. We then investigate
 three-dimensional systems\, providing useful benchmarks for
 even-spaced discretization. We conclude with a discussion of current
 challenges and potential solutions for scaling diagonal basis sets\,
 which is an early but promising area of research.
LOCATION:Haldeman 031
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DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3eff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260824T160000
CATEGORIES:Special Event
SUMMARY:$\\LaTeX$ title with $\\textit{italics}$
LOCATION:Kemeny 102b
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BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3f37@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260910T090000
DTEND;TZID=America/New_York:20260910T100000
CATEGORIES:Special Event
SUMMARY:Math Department Open House for First-Year Students
LOCATION:Kemeny Basement Level
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BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3f6b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260922T173000
CATEGORIES:∾ Prosser Lecture ∾
SUMMARY:David Mumford: Reopening the study of the Foundations of
 Math
DESCRIPTION:It is standard nowadays to start with Zermelo-Fraenkel
 set\ntheory and build all math on top of this. But the development
 of set\ntheory has produced a long sequence of alternate models with
 new axioms\nof infinity and of infinite games. On the other hand\,
 core mathematics\nrequires its conjectures always to have definite
 truth values\, yes or\nno. How can you work a problem if it might be
 true in some worlds\, false\nin others. This means core math
 requires a base model of “tangible”\nthings where every
 conjecture has an answer\, where you need not worry\nabout vast
 set-theoretic infinities and infinite games.  Sy Friedman and\nI
 have had long discussions about this and came up a proposal for
 new\nand simpler foundations that I will present.
LOCATION:Kemeny 006
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DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf3fd1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260923T180000
CATEGORIES:∾ Prosser Lecture ∾
SUMMARY:David Mumford: Comparing AIs and the Human Brain: the
 challenge of Agency
DESCRIPTION:AIs started with “neural nets” in the 1940s\,
 inspired by\nneurons and the brain continues to have many parallels
 to AI with the\nintroduction of transformers and scalability. I
 believe that future AIs\nwill benefit by borrowing more ideas from
 the brain and from human life.\nLooking at human development\, it is
 not until age 18 (or 21) that people\nare considered adults\, hence
 given rights to act as they wish. They are\nthen given Agency\, to
 plan and take actions in the world freely.\nSilicon Valley today
 assumes that limited agency can be grafted on large\nlanguage models
 easily. But is that true? The purpose of this talk is to\nanalyze
 what seems to be missing.
LOCATION:Kemeny 008
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DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf401f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20260924T151500
CATEGORIES:Math Colloquium
SUMMARY:Ismar Volić: TBD
LOCATION:Kemeny 007
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BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf4054@math.dartmouth.edu
DTSTART;TZID=America/New_York:20261008T160000
CATEGORIES:Math Colloquium
SUMMARY:Shai Pilosof: TBD
LOCATION:Kemeny 007
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BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf4087@math.dartmouth.edu
DTSTART;TZID=America/New_York:20261029T151500
CATEGORIES:Math Colloquium
SUMMARY:John Etnyre: TBD
LOCATION:Kemeny 007
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DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf40bb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20261112T151500
CATEGORIES:Math Colloquium
SUMMARY:Alberto Abbondandolo: TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf40ee@math.dartmouth.edu
DTSTART;TZID=America/New_York:20270211T151500
CATEGORIES:Math Colloquium
SUMMARY:Eric Egge: TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf4121@math.dartmouth.edu
DTSTART;TZID=America/New_York:20270217T190000
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Ciprian Manolescu: TBD
DESCRIPTION:(Time TBD)
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260814T161700Z
UID:20260814T1617006a7f3f7cf415b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20270218T151500
CATEGORIES:Math Colloquium
SUMMARY:Ciprian Manolescu: TBD
LOCATION:TBD
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