Toric Varieties Fan Club: Difference between revisions
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14 weeks total, starting on January 25, adjusting throughout the semester as necessary. | 14 weeks total, starting on January 25, adjusting throughout the semester as necessary. | ||
Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading, led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [https://uwmadison.zoom.us/j/ | Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading (about 10 pages), led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [https://uwmadison.zoom.us/j/94806372074]. | ||
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'''Week 1''' | '''Week 1''' | ||
Monday, January 25: Ch. 1.0 Affine Varieties Background (Speaker: | Monday, January 25: Ch. 1.0 Affine Varieties Background (Speaker: Ola Sobieska) | ||
Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties (Speaker: Ola Sobieska) | Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties (Speaker: Ola Sobieska) | ||
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'''Week 2''' | '''Week 2''' | ||
Monday, February 1: Ch. 1.2 Cones and Affine Toric Varieties (Speaker: | Monday, February 1: Ch. 1.2 Cones and Affine Toric Varieties (Speaker: Ivan Aidun) | ||
Wednesday, February 3: Ch. 1.3 Properties of Affine Toric Varieties (Speaker: | Wednesday, February 3: Ch. 1.3 Properties of Affine Toric Varieties (Speaker: Ola Sobieska) | ||
'''Week 3''' | '''Week 3''' | ||
Monday, February 8: Ch. 2.1 Lattice Points and Projective Toric Varieties (Speaker: | Monday, February 8: Ch. 2.1 Lattice Points and Projective Toric Varieties (Speaker: Zinan Wang) | ||
Wednesday, February 10: Ch. 2.2 Lattice Points and Polytopes (Speaker: Maya Banks) | |||
'''Week 4''' | '''Week 4''' | ||
Monday, February 15: Ch. 2.3 Polytopes and Projective Toric Varieties (Speaker: | Monday, February 15: Ch. 2.3 Polytopes and Projective Toric Varieties (Speaker: Will Hardt) | ||
Wednesday, February 17: Ch. 2.4 Properties of Projective Toric Varieties (Speaker: | Wednesday, February 17: Ch. 2.4 Properties of Projective Toric Varieties (Speaker: Ivan Aidun) | ||
| Line 45: | Line 46: | ||
Monday, February 22: Catch-up/Review Day | Monday, February 22: Catch-up/Review Day | ||
Wednesday, February 24: Ch. 3.1 Fans and Normal Toric Varieties (Speaker: | Wednesday, February 24: Ch. 3.1 Fans and Normal Toric Varieties (Speaker: Caitlyn Booms) | ||
'''Week 6''' | '''Week 6''' | ||
Monday, March 1: Ch. 3.2 The Orbit-Cone Correspondence (Speaker: | Monday, March 1: Ch. 3.2 The Orbit-Cone Correspondence (Speaker: Zinan Wang) | ||
Wednesday, March 3: Ch. 3.3 Toric Morphisms (Speaker: | Wednesday, March 3: Ch. 3.3 Toric Morphisms (Speaker: Ola Sobieska) | ||
'''Week 7''' | '''Week 7''' | ||
Monday, March 8: Ch. 3.4 Complete and Proper (Speaker: | Monday, March 8: Ch. 3.4 Complete and Proper (Speaker: Ola Sobieska) | ||
Wednesday, March 10: Catch-up/Review Day | Wednesday, March 10: Catch-up/Review Day | ||
| Line 64: | Line 65: | ||
'''Week 8''' | '''Week 8''' | ||
Monday, March 15: Ch. 4.0 Valuations, Divisors, and Sheaves Background (Speaker: | Monday, March 15: Ch. 4.0 Valuations, Divisors, and Sheaves Background (Speaker: Will Hardt) | ||
Wednesday, March 17: Ch. 4.1 Weil Divisors on Toric Varieties (Speaker: | Wednesday, March 17: Ch. 4.1 Weil Divisors on Toric Varieties (Speaker: Maya Banks) | ||
'''Week 9''' | '''Week 9''' | ||
Monday, March 22: Ch. 4.2 Cartier Divisors on Toric Varieties (Speaker: | Monday, March 22: Ch. 4.2 Cartier Divisors on Toric Varieties (Speaker: Ola Sobieska) | ||
Wednesday, March 24: Ch. 4.3 The Sheaf of a Torus-Invariant Divisor (Speaker: | Wednesday, March 24: Ch. 4.3 The Sheaf of a Torus-Invariant Divisor (Speaker: Caitlyn Booms) | ||
'''Week 10''' | '''Week 10''' | ||
Monday, March 29: Ch. 5.0 Quotients in Algebraic Geometry Background (Speaker: | Monday, March 29: Ch. 5.0 Quotients in Algebraic Geometry Background (Speaker: Ivan Aidun) | ||
Wednesday, March 31: Ch. 5.1 Quotient Constructions of Toric Varieties (Speaker: | Wednesday, March 31: Ch. 5.1 Quotient Constructions of Toric Varieties (Speaker: Caitlyn Booms) | ||
'''Week 11''' | '''Week 11''' | ||
Monday, April 5: Ch. 5.2 The Total Coordinate Ring (Speaker: | Monday, April 5: Ch. 5.2 The Total Coordinate Ring (Speaker: Maya Banks) | ||
Wednesday, April 7: Ch. 5.3 Sheaves on Toric Varieties (Speaker: | Wednesday, April 7: Ch. 5.3 Sheaves on Toric Varieties (Speaker: Will Hardt) | ||
'''Week 12''' | '''Week 12''' | ||
Monday, April 12: Ch. 5.4 Homogenization and Polytopes (Speaker: | Monday, April 12: Ch. 5.4 Homogenization and Polytopes (Speaker: Ola Sobieska) | ||
Wednesday, April 14: Ch. 6.0 Sheaves and Line Bundles Background (Speaker: | Wednesday, April 14: Ch. 6.0 Sheaves and Line Bundles Background (Speaker: Caitlyn Booms) | ||
| Line 101: | Line 102: | ||
Monday, April 19: Ch. 6.1 Ample and Basepoint Free Divisors on Complete Toric Varieties (Speaker: TBD) | Monday, April 19: Ch. 6.1 Ample and Basepoint Free Divisors on Complete Toric Varieties (Speaker: TBD) | ||
Wednesday, April 21: Ch. 6.2 Polytopes and Projective Toric Varieties (Speaker: | Wednesday, April 21: Ch. 6.2 Polytopes and Projective Toric Varieties (Speaker: Maya Banks) | ||
'''Week 14''' | '''Week 14''' | ||
Monday, April 26: | Monday, April 26: Guest Lecture (Speaker: Daniel Erman) | ||
Wednesday, April 28: Ch. 6.3 The Nef and Mori Cones (Speaker: TBD) | |||
== General Meeting Structure == | == General Meeting Structure == | ||
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be | This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be a professor or other guest speaker. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We may also use Macaulay2 during the exercise portions to get comfortable both computing examples by hand and by using a computer. | ||
'''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu by | '''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu or Aleksandra (Ola) Sobieska at asobieska@wisc.edu by January 24, 2021.''' | ||
Latest revision as of 02:16, 13 April 2021
This is the page for the Spring 2021 Toric Varieties Fan Club (Reading Group), which is open to all UW Math grad students, but will require a certain amount of participation and work to receive course credit (details below).
Resources
We plan to read Cox, Little, and Schenck's Toric Varieties, which can be downloaded here: [1].
Meeting Schedule
14 weeks total, starting on January 25, adjusting throughout the semester as necessary.
Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading (about 10 pages), led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [2].
Optimistic Reading Schedule:
Week 1
Monday, January 25: Ch. 1.0 Affine Varieties Background (Speaker: Ola Sobieska)
Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties (Speaker: Ola Sobieska)
Week 2
Monday, February 1: Ch. 1.2 Cones and Affine Toric Varieties (Speaker: Ivan Aidun)
Wednesday, February 3: Ch. 1.3 Properties of Affine Toric Varieties (Speaker: Ola Sobieska)
Week 3
Monday, February 8: Ch. 2.1 Lattice Points and Projective Toric Varieties (Speaker: Zinan Wang)
Wednesday, February 10: Ch. 2.2 Lattice Points and Polytopes (Speaker: Maya Banks)
Week 4
Monday, February 15: Ch. 2.3 Polytopes and Projective Toric Varieties (Speaker: Will Hardt)
Wednesday, February 17: Ch. 2.4 Properties of Projective Toric Varieties (Speaker: Ivan Aidun)
Week 5
Monday, February 22: Catch-up/Review Day
Wednesday, February 24: Ch. 3.1 Fans and Normal Toric Varieties (Speaker: Caitlyn Booms)
Week 6
Monday, March 1: Ch. 3.2 The Orbit-Cone Correspondence (Speaker: Zinan Wang)
Wednesday, March 3: Ch. 3.3 Toric Morphisms (Speaker: Ola Sobieska)
Week 7
Monday, March 8: Ch. 3.4 Complete and Proper (Speaker: Ola Sobieska)
Wednesday, March 10: Catch-up/Review Day
Week 8
Monday, March 15: Ch. 4.0 Valuations, Divisors, and Sheaves Background (Speaker: Will Hardt)
Wednesday, March 17: Ch. 4.1 Weil Divisors on Toric Varieties (Speaker: Maya Banks)
Week 9
Monday, March 22: Ch. 4.2 Cartier Divisors on Toric Varieties (Speaker: Ola Sobieska)
Wednesday, March 24: Ch. 4.3 The Sheaf of a Torus-Invariant Divisor (Speaker: Caitlyn Booms)
Week 10
Monday, March 29: Ch. 5.0 Quotients in Algebraic Geometry Background (Speaker: Ivan Aidun)
Wednesday, March 31: Ch. 5.1 Quotient Constructions of Toric Varieties (Speaker: Caitlyn Booms)
Week 11
Monday, April 5: Ch. 5.2 The Total Coordinate Ring (Speaker: Maya Banks)
Wednesday, April 7: Ch. 5.3 Sheaves on Toric Varieties (Speaker: Will Hardt)
Week 12
Monday, April 12: Ch. 5.4 Homogenization and Polytopes (Speaker: Ola Sobieska)
Wednesday, April 14: Ch. 6.0 Sheaves and Line Bundles Background (Speaker: Caitlyn Booms)
Week 13
Monday, April 19: Ch. 6.1 Ample and Basepoint Free Divisors on Complete Toric Varieties (Speaker: TBD)
Wednesday, April 21: Ch. 6.2 Polytopes and Projective Toric Varieties (Speaker: Maya Banks)
Week 14
Monday, April 26: Guest Lecture (Speaker: Daniel Erman)
Wednesday, April 28: Ch. 6.3 The Nef and Mori Cones (Speaker: TBD)
General Meeting Structure
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be a professor or other guest speaker. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We may also use Macaulay2 during the exercise portions to get comfortable both computing examples by hand and by using a computer.
If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu or Aleksandra (Ola) Sobieska at asobieska@wisc.edu by January 24, 2021.