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27      <a href=champ/index.html>CHAMP</a>
28      <a href=https://nebraskacommalg.github.io/RTG/conferences/reu.html>International REU</a>      
29      <a href=https://nebraskacommalg.github.io/RTG/seminar.html>UNL Commutative Algebra Seminar</a>
30      <a href=https://eloisagrifo.github.io/conferences/camp.html>Summer CAMP</a>
31      <a href=https://eloisagrifo.github.io/conferences/bhargav.html>Commutative algebra in mixed characteristic</a>
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54        <TITLE>
55            Elo&iacute;sa Grifo | Talk notes
56        </TITLE>
57        <LINK REV="made" HREF="mailto:grifo&#x40;unl.edu">
58
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60
61
62
63 
64<h2><center>Notes on symbolic powers</center></h2>
65
66
67Here is video of a talk on symbolic powers I gave at the <a href=https://sites.google.com/view/fellowship-of-the-ring/>Fellowship of the ring</a>, the virtual Worldwide Commutative Algebra Seminar, hosted by MSRI.
68<br>
69<br>
70<center> 
71<iframe width="560" height="315" src="https://www.youtube.com/embed/Be83xC1isy4" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
72</center>
73<br>
74<br>
75
76
77
78
79I've written several sets of lecture notes on symbolic powers. All of these are drafts and are highly likely to contain typos.
80
81
82
83
84<br><br>
85
86<b>Notes directed at advanced commutative algebra graduate students:</b>
87<br>
88The following are notes I wrote for a semester long course on symbolic powers at the University of Nebrask&mdash;Lincoln:
89<br><br>
90<center><a href=SymbolicPowers.pdf>Main symbolic powers notes</a></center>
91<br>
92These are likely to still contain typos, but these are the most up-to-date notes I have written on the subject.
93<br><br>
94I have also written shorter notes for week-long courses. The notes below were written for the <a href=http://ac2019.eventos.cimat.mx>Escuela de oto&ntilde;o de &Agrave;lgebra Conmutativa</a> at <a href=https://www.cimat.mx>CIMAT</a> in November 2019 organized by <a href="http://www.cimat.mx/~luisnub/home.html">Luis N&uacute;&ntilde;ez-Betancourt</a> and <a href=http://personal.cimat.mx:8181/~abraham.mc/Home.html>Abraham Mart&iacute;n del Campo</a>, and earlier for the <a href="https://www.math.utah.edu/agtrtg/commutative-algebra/
95">RTG Advanced Mini-course in Commutative Algebra</a> at the University of Utah in May 2018, organized by <a href=https://www.math.utah.edu/~singh/>Anurag K. Singh</a> and <a href=https://www.math.utah.edu/~iyengar/>Srikanth B. Iyengar</a>. The <a href="SymbolicPowersUtah.pdf">older version of my notes on symbolic powers</a> is no longer kept updated, so I'd recommend reading the newer version below. While the CIMAT lectures were delivered in spanish, the main version of the notes is the English version, and the others are more or less translations of the English version.
96
97<br><br>
98<center>
99<a href="SymbolicPowersCIMAT.pdf">english version</a> 
100&nbsp;
101<a href="SymbolicPowersEspanol.pdf">versi&oacute;n en espa&ntilde;ol</a> 
102&nbsp;
103<a href="SymbolicPowersTuga.pdf">vers&atilde;o em portugu&ecirc;s</a>
104</center>
105
106<br><br>
107
108<b>Notes directed at advanced undergraduates:</b>
109<br>
110These are the materials for the lecture series I gave at <a href=http://www.math.utah.edu/awmchapter/conference/>BRIDGES</a>, a conference aimed towards early graduate students and advanced undergraduate students interested in representation theory, number theory, and commutative algebra, hosted by the University of Utah AWM student chapter. These lectures assumed only a first course in algebra, and no commutative algebra background.
111
112<br><br>
113<center>
114<a href=bridges/bridges.pdf>Lecture notes</a>
115&nbsp; &nbsp;
116<a href=bridges/BridgesProblems.pdf>Problem list</a>
117&nbsp; &nbsp;
118<a href=bridges/bridges1.pdf>Day 1</a>
119&nbsp; &nbsp;
120<a href=bridges/bridges2.pdf>Day 2</a>
121&nbsp; &nbsp;
122<a href=bridges/bridges3.pdf>Day 3</a>
123</center>
124
125
126
127<br>
128
129<h2><center>Other videos from research talks</h2>
130
131
132
133
134<a href=https://icerm.brown.edu/video_archive/?play=2651>Symbolic powers in mixed characteristic</a>, at the ICERM workshop <a href=https://icerm.brown.edu/topical_workshops/tw-21-dmga/>D-modules, Group Actions, and Frobenius: Computing on Singularities</a>
135
136<br><br>
137
138<div class="row">
139  <div class="column1">
140<center>
141<br><br><br><br><br>
142<a href=Talks/OaxacaMixedChar.pdf>Symbolic powers in mixed characteristic</a>
143<br> 
144in
145<br>
146<a href=https://www.birs.ca/events/2022/5-day-workshops/22w5174>BIRS workshop on advances in mixed char</a> 
147<br>
148May 10, 2022
149</center>
150</div>
151<div class="column2">
152
153<iframe width="512" height="288" src="http://www.birs.ca/events/2022/5-day-workshops/22w5174/videos/embed/202205100915-Grifo.mp4" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
154
155</div></div>
156</li>
157
158
159<div class="row">
160  <div class="column1">
161<center>
162<br><br><br><br><br>
163<a href=Talks/FRGUtah2021.pdf>Symbolic powers in mixed characteristic</a>
164<br> 
165in
166<br>
167<a href=https://sites.google.com/view/special-month-on-singularities/home>Special Month On Singularities & K-Stability</a>
168<br>
169June 6, 2021
170</center>
171</div>
172<div class="column2">
173
174<iframe width="512" height="288" src="https://www.youtube.com/embed/9UUmgDbhjbc" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
175
176</div></div>
177</li>
178
179
180<div class="row">
181  <div class="column1">
182<center>
183<br><br><br><br><br>
184<a href=Talks/MCA2021.pdf>Differential powers in mixed characteristic</a>
185<br> 
186in
187<br>
188<a href=https://www.mca2021.org/en/special-sessions/item/55-differential-operators-in-algebraic-geometry-and-commutative-algebra>Special Session on differential operators in algebraic geometry and commutative algebra</a> at the <a href=https://www.mca2021.org/en/>2021 MCA</a>
189<br>
190July 16, 2021
191</center>
192</div>
193<div class="column2">
194
195<iframe width="512" height="288" src="https://www.youtube.com/embed/LUWQ0zHyGY4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
196
197</div></div>
198</li>
199
200
201
202
203
204<br><br><br>
205
206
207
208 <H2><center>
209            Notes and slides from research talks</center>
210        </H2>
211
212
213<ul>
214
215
216<li>
217<a href=Talks/OaxacaMixedChar.pdf>Symbolic powers in mixed characteristic</a>
218&nbsp;
219(<a href=https://www.birs.ca/events/2022/5-day-workshops/22w5174>BIRS workshop on advances in mixed char</a>, 05/10/2022)
220<br>
221</li>
222
223
224<li>
225<a href=Talks/CA+.pdf>Cohomological Support Varieties</a>
226&nbsp;
227(<a href=http://www.fields.utoronto.ca/activities/21-22/CAAC2022>CA+</a> at Iowa State, 05/01/2022, and <a href=https://math.unl.edu/kumunu-2021>KUMUNU</a> at UNL, 05/08/2022)
228<br>
229</li>
230
231
232
233<li>
234<a href=Talks/CAAC2022.pdf>Symbolic powers</a>
235&nbsp;
236(<a href=http://www.fields.utoronto.ca/activities/21-22/CAAC2022>
236Combinatorial Algebra meets Algebraic Combinatorics</a> at the Fields Institute, 01/23/2022)
237<br>
238</li>
239
240
241<li>
242<a href=Talks/ICERM2021.pdf>Symbolic powers in mixed characteristic</a>
243&nbsp;
244(ICERM workshop <a href=https://icerm.brown.edu/topical_workshops/tw-21-dmga/>D-modules, Group Actions, and Frobenius: Computing on Singularities</a>, 08/12/2021)
245<br>
246</li>
247
248
249<li>
250<a href=Talks/MCA2021.pdf>Differential powers in mixed characteristic</a>
251&nbsp;
252(<a href=https://www.mca2021.org/en/special-sessions/item/55-differential-operators-in-algebraic-geometry-and-commutative-algebra>Special session on Differential operators in CA and AG</a> at the <a href=https://www.mca2021.org/en/>Mathematical Congress of the Americas</a>, 07/16/2021)
253<br>
254</li>
255
256
257<li>
258<a href=Talks/FRGUtah2021.pdf>Symbolic powers in mixed characteristic</a>
259&nbsp;
260(<a href=https://sites.google.com/view/special-month-on-singularities/home>Special Month On Singularities & K-Stability</a> 06/07/2021)
261<br>
262</li>
263
264
265<li>
266<a href=Talks/NotreDame2021.pdf>Test modules for the complete intersection property</a>
267&nbsp;
268(Notre Dame AG/CA Seminar 04/27/2021)
269<br>
270</li>
271
272
273<li>
274<a href=Talks/AMS2021Cincinnati.pdf>Test modules for the complete intersection property</a>
275&nbsp;
276(Special Session on <a href=https://www.ams.org/meetings/sectional/2286_program_ss7.html#title>Commutative Algebra</a> at the <a href=https://www.ams.org/meetings/sectional/2286_program.html>Cincinnati Virtual AMS Sectional Meeting</a>.)
277<br>
278</li>
279
280
281<li>
282<a href=Talks/AMS2021Brown.pdf>Constructing non-proxy small modules</a>
283&nbsp;
284(Special Session on <a href=http://www.ams.org/meetings/sectional/2284_program_ss1.html#title>Commutative Algebra</a> at the <a href=http://www.ams.org/meetings/sectional/2284_special.html>Brown Virtual AMS Sectional Meeting</a>)
285<br>
286</li>
287
288
289
290<li>
291<a href=Talks/Mulheres.pdf>Symbolic Powers</a>
292&nbsp;
293(Mulheres Matem&aacute;ticas: uma tarde de encontro)
294<br>
295</li>
296
297
298<li>
299<a href=Talks/UNLOctober2020.pdf>Constructing non-proxy small modules</a>
300&nbsp;
301(UNL Commutative Algebra Seminar)
302<br>
303</li>
304
305
306<li>
307<a href=Talks/AMS2020October.pdf>Constructing non-proxy small modules</a>
308&nbsp;
309(<a href=http://www.ams.org/meetings/sectional/2278_program_ss5.html#title>Special Session on Homological Methods in Algebra</a> at the Virtual Fall AMS Sectional Meeting 2020)
310<br>
311</li>
312
313
314
315<li>
316<a href=Talks/FOTR.pdf>Symbolic Powers, stable containments, and degree bounds</a>
317&mdash; these notes correspond to the <a href=https://www.youtube.com/watch?v=Be83xC1isy4>video</a> above
318&nbsp;
319(<a href=https://www.msri.org/general_events/24976>Fellowship of the ring, worldwide seminar</a>)
320<br>
321</li>
322
323
324
325
326<li>
327<a href=Talks/SwitzerlandZoom.pdf>Symbolic Powers and the (stable) containment problem</a>
328&nbsp;
329(Bern/Fribourg/Neuch&acirc;tel InterCity Seminar)
330<br></li>
331
332
333
334
335<li>
336<a href=Talks/TulaneColloquium.pdf>Symbolic Powers</a>
337&nbsp;
338(Tulane University Colloquium)
339<br></li>
340
341
342<li>
343<a href=Talks/TulaneAlgebra.pdf>Symbolic Powers and the (stable) containment problem</a>
344&nbsp;
345(Tulane University Algebra and Combinatorics Seminar)
346<br></li>
347
348
349<li>
350<a href=Talks/UNLColloquium2020.pdf>Symbolic Powers</a>
351&nbsp;
352(University of Nebraska &#8212; Lincoln Colloquium)
353<br></li>
354
355
356<li>
357<a href=Talks/UIC2019.pdf>A stable version of Harbourne's Conjecture</a>
358&nbsp;
359(University of Illinois at Chicago Commutative Algebra Seminar)
360<br></li>
361
362
363<li>
364Symbolic powers and <a href=Talks/UNLCAFall2019.pdf>Two versions of Harbourne's Conjecture</a> (2 part talk)
365&nbsp;
366(University of Nebraska &#8212; Lincoln Commutative Algebra Seminar)
367<br></li>
368
369<li>
370<a href=Talks/UtahAugust2019.pdf>A stable version of Harbourne's Conjecture</a>
371&nbsp;
372(University of Utah Commutative Algebra Seminar)
373<br></li>
374
375
376<li>
377<a href=Talks/Wisconsin2019.pdf>Symbolic powers and the (stable) containment problem</a>
378&nbsp;
379(University of Wisconsin Madison Algebra and Algebraic Geometry Seminar)
380<br></li>
381
382
383
384<li>
385<a href=Talks/MorgantownAlgebraDays2019.pdf>A Fedder-type criterion over Gorenstein rings</a>
386&nbsp;
387(<a href=https://math.wvu.edu/mad2019/>Morgantown Algebra Days</a>)
388<br></li>
389
390
391
392<li>
393<a href=Talks/CentralMichiganSeminar.pdf>Symbolic powers and the containment problem</a>
394&nbsp;
395(Central Michigan Algebra and Combinatorics Seminar)
396<br></li>
397
398
399
400<li>
401<a href=Talks/Colloquium2019.pdf>Symbolic powers</a>
402&nbsp;
403(UC Riverside Colloquium and Oklahoma State Colloquium)
404<br></li>
405
406
407<li>
408<a href=Talks/OberwolfachFebruary2019.pdf>A Fedder-type criterion over Gorenstein rings and symbolic powers</a>
409&nbsp;
410(Oberwolfach Workshop on <A href="https://www.mfo.de/occasion/1907/www_view">Singularities and Homological Aspects of Commutative Algebra</A>)
411<br></li>
412
413
414<li>
415<a href=Talks/CMSWinter.pdf>A stable version of Harbourne's Conjecture</a>
416&nbsp;
417(<a href=https://cms.math.ca/Events/winter18/schedule_session#srp>Special Session on Symbolic and regular powers of ideals</a> at the CMS Winter Meeting 2018)
418<br></li>
419
420
421
422<li>
423<a href=Talks/MichiganAMSDevelopments.pdf>Symbolic powers of ideals defining F-pure rings</a>
424&nbsp;
425(<a href=http://www.ams.org/meetings/sectional/2259_program_ss15.html#title>Special Session on Advances in Commutative Algebra</a> at the Ann Arbor AMS Meeting 2018)
426<br></li>
427
428
429<li>
430<a href=Talks/MichiganAMSComplexity.pdf>Symbolic powers and free resolutions</a>
431&nbsp;
432(<a href=http://www.ams.org/meetings/sectional/2259_program_ss32.html#title>Special Session on Commutative Algebra and complexity</a> at the Ann Arbor AMS Meeting 2018)
433<br></li>
434
435
436<li>
437<a href=Talks/OberwolfachOctober2018.pdf>A stable version of Harbourne's Conjecture</a>
438&nbsp;
439(<a href=https://www.mfo.de/occasion/1840b/www_view>
439MFO Mini-workshop on Asymptotic invariants of homogeneous ideals</a> 2018)
440<br></li>
441
442
443
444<li>
445<a href=Talks/Kumunujr2018.pdf>Homological algebra vs symbolic powers</a>
446&nbsp;
447(<a href=http://www.math.unl.edu/~jpollitz2/KUMUNUJr18/>KUMUNUjr</a> 2018)
448<br></li>
449
450
451 <li>
452<a href=Talks/BostonAMS.pdf>Applying homological algebra to a problem on symbolic powers</a>
453&nbsp;
454(Boston AMS Meeting Special Session on Homological Methods in Commutative Algebra)
455<br></li>
456
457
458 <li>
459<a href=Talks/PortlandAMS.pdf>Symbolic powers and the containment problem</a>
460&nbsp;
461(<a href=http://www.ams.org/meetings/sectional/2248_program_ss5.html#title>Special Session on Commutative Algebra</a> at the Portland AMS Meeting)
462<br></li>
463
464
465 <li>
466<a href=Talks/DefenseTalk.pdf>Symbolic powers and the containment problem</a>
467&nbsp;
468(PhD thesis defense)
469<br></li>
470
471
472 <li>
473<a href=Talks/OhioAMS.pdf>The Zariski-Nagata theorem in mixed characteristic</a>
474&nbsp;
475(AMS Sectional Meeting in Ohio, <A href="http://www.ams.org/meetings/sectional/2250_program_ss18.html#title">Special Session in Commutative and Combinatorial Algebra</A>)
476<br></li>
477
478
479 <li>
480<a href=Talks/JMM2018.pdf>Symbolic powers: the Containment Problem and Harbourne's Conjecture</a>
481&nbsp;
482(Joint Math Meetings, <A href="http://jointmathematicsmeetings.org/meetings/national/jmm2018/2197_program_ss67.html">Special Session in Commutative Algebra in All Characteristics</A>)
483<br></li>
484
485
486 <li>
487<a href=Talks/GeorgeMason2017.pdf>Symbolic powers and differential operators</a>
488&nbsp;
489(George Mason University Combinatorics, Algebra and Geometry Seminar)
490<br></li>
491
492
493
494 <li>
495<a href=Talks/KUNovember2017.pdf>Symbolic powers and the Containment Problem</a>
496&nbsp;
497(University of Kansas Algebra Seminar)
498<br></li>
499
500
501 <li>
502<a href=Talks/SouthCarolinaNovember2017.pdf>Symbolic powers and the Containment Problem</a> (2 hour talk)
503&nbsp;
504(University of South Carolina Algebraic Geometry Seminar)
505<br></li>
506
507
508 <li>
509<a href=Talks/NMSUOctober2017.pdf>Symbolic powers and differential operators</a>
510&nbsp;
511(New Mexico State University Algebra Seminar)
512<br></li>
513
514
515  <li>
516<a href=Talks/Orlando-AMS.pdf>A stable version of Harbourne's Conjecture</a>
517&nbsp;
518(AMS sectional meeting in Orlando, Florida, <A href="http://www.ams.org/meetings/sectional/2246_program_ss1.html#title">Special Session on Commutative Algebra</A>)
519<br></li>
520
521  <li>
522<a href=Talks/Denton-AMS.pdf>A stable version of Harbourne's Conjecture</a>
523&nbsp;
524(AMS sectional meeting in Denton, Texas, <A href="http://www.ams.org/meetings/sectional/2249_program_ss10.html#title">Special Session on Commutative Algebra</A>)
525<br>
526  </li>
527
528
529  <li>
530<a href=Talks/NYC-AMS.pdf>Symbolic powers of ideals defining F-pure rings</a>
531&nbsp;
532(AMS sectional meeting in New York, New York, <A href="http://www.ams.org/meetings/sectional/2242_program_ss1.html#title">Special Session on Commutative Algebra</A>)
533<br>
534  </li>
535
536
537   <li>
538<a href=Talks/UtahApril2017.pdf>Symbolic powers of ideals defining F-pure rings</a>
539&nbsp;
540(University of Utah Commutative Algebra Seminar)
541
542
543   <li>
544<a href=Talks/SC-AMS.pdf>Symbolic powers of ideals defining F-pure rings</a>
545&nbsp;
546(AMS sectional meeting in Charleston, SC, <A href="http://www.ams.org/meetings/sectional/2228_program_ss1.html#title">Special Session on Commutative Algebra</A>)
547<br>
548  </li>
549
550
551 <li>
552<a href=Talks/NebraskaMarch2017.pdf>Symbolic powers in characteristic p</a> (2 hour talk)
553&nbsp;
554(University of Nebraska &#8212; Lincoln Commutative Algebra Seminar)
555<br></li>
556
557
558
559
560<li>
561<a href=Talks/ClemsonMarch2017.pdf>Symbolic powers</a>
562&nbsp;
563(Clemson University Algebra and Discrete Math Seminar)
564<br></li>
565
566
567 <li>
568<a href=Talks/MichiganJanuary2017.pdf>Symbolic powers of ideals defining F-pure rings</a>
569&nbsp;
570(University of Michigan Commutative Algebra Seminar)
571<br></li>
572</ul>
573
574
575<br>
576<br>
577
578
579<p align=center>
580<img src=eloisatalk2.jpeg height=250 hspace=50>
581<img src=eloisatalk3.jpeg height=250 hspace=50>
582</p>
583
584
585<br>
586<br>
587
588
589 <H2><center>
590            Notes and slides from expository talks and talks directed at undergraduates</center>
591        </H2>
592
593
594<ul>
595
596
597<li>
598<a href=Talks/UCRGrad.pdf>A story of algebra vs geometry</a>
599&nbsp;
600(UCR Graduate Open House, November 2020)
601<br>
602</li>
603
604
605<li>
606<a href=Talks/BIKES2020charp.pdf>Frobenius or: how I learned to stop worrying and love characteristic p</a>
607&nbsp;
608(BIKES, University of Utah Commutative Algebra Student Seminar, January 2020)
609<br></li>
610
611<li>
612<a href=Talks/UndergraduateSymposium.pdf>Symbolic powers and a story of algebra vs geometry</a>
613&nbsp;
614(<a href=https://homepages.math.uic.edu/ums/>Undergraduate Research Symposium</a>, UIC, November 2019)
615<br></li>
616
617
618<li>
619<a href=Talks/StudentCASemUM2019.pdf>Symbolic powers</a>
620&nbsp;
621(University of Michigan Graduate Student Commutative Algebra Seminar, Winter of 2019)
622<br></li>
623
624
625
626<li>
627<a href=Talks/UMichMathClub2019.pdf>Slicing a square pizza</a>
628&nbsp;
629(University of Michigan Math Club, Winter of 2019)
630<br></li>
631
632
633<li>
634<a href=Talks/SingularitiesCharp.pdf>An introduction to singularities in characteristic p: Frobenius is your friend</a>
635&nbsp;
636(Reading course on singularities organized by <a href=http://www-personal.umich.edu/~malloryd/>Devlin Mallory</a> at UMich in the Fall of 2018)
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645<p class="caption"><center>
646	email: grifo&#64;unl.edu &nbsp; | &nbsp; Office: 339 Avery Hall
647</center> </p>
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